Homework Help for Statistics

A security and metal detection machine at an airport has a service rate that follows an exponential distribution with μ = 10 minutes.

Passengers arrive at the machine with an exponential rate of λ = 8 minutes. The queuing rule is FCFS. Find the expected machine utilisation, passenger throughput time, and average waiting time.

Suppose three students are selected at random. Let A be the random 
variable representing the number of ABM students that are selected.

16. What is the probability that there will be no ABM student selected?
A. 8/27      B. 4/9      C. 19/27      D. 1

17. What is the probability that at most 2 ABM students are selected? (2 points)
A. 0      B. 0.2222      C. 0.4444      D. 0.9630

18. What is the probability that less than 2 ABM students are selected? (2 points)
A. 0.2222      B. 0.7407      C. 0.9630      D. 1

19. What is the mean of the probability distribution of the random variable A? (2 
points)
A. 0.5      B. 0.67      C. 1      D. 1.3

20. What is the variance of the probability distribution of the random variable A? (2 
points)
A. 0      B. 0.33      C. 0.44      D. 0.66

Suppose four students are selected at random from the gathered date. Let C 
be the random variable representing the number of CBL students that are selected.

8. How many sample points can be generated from the experiment?
A. 2       B. 4       C. 16       D. 20

9. What are the values of the random variable C?
A. 0, 1, 2, 3, 4 C. 0.0625, 0.25, 0.375
B. 1, 1, 4, 4, 6 D. O and C

10. What is the probability that 2 CBL students are selected?
A. 3/16       B. 3/14       C. 3/12       D. 3/8

11. What is the probability that all students selected are OBL?
A. 0 B. 0.0625 C. 0.25 D. 1

12. What is the probability that 3 or more CBL students are selected? (2 points)
A. 0       B. 0.0625       C. 0.25       D. 0.3125

13. What is the average number of CBL students that have been selected? (2 points)
A. 1       B. 2       C. 3       D. 4

14. What is the standard deviation of the probability distribution of the number of 
CBL students that has been selected? (2 points)
A. 0.5       B. 0.75       C. 1       D. 1.25

What is the population of interest of the study?
A. Student’s General Weighted Average and their stress level
B. School Administration
C. Senior High School students
D. Analysis of the gathered data.
2. Which of the following pertains to inferential statistics?
A. Conducting a hypothesis test to test if there is a difference on the stress level 
of senior high school students when grouped according to strand.
B. Presenting a graphical report on the General Weighted Average of senior high 
school students.
C. Gathering the data on the General Weighted Average and stress level of 
students.
D. Summarizing the gathered data on the General Weighted Average and stress 
level of students.
3. Which of the following is a parameter?
A. The GWA of 181 senior high students.
B. The GWA of 29 HUMSS students.
C. The GWA of some senior high students.
D. The GWA of all senior high students of SLU-LHS-SH

Why some people don't want the covid 19 vaccine?

18. Suppose that the vehicle speeds at an interstate location have a normal distribution with a mean equal to 70mph and a standard deviation equal to 8mph. What is the z-score for a speed of 68mph? (2 points)  
A.z=−0.35z=−0.35       B.z=−0.55z=−0.55       C.z=−0.25z=−0.25       D.z=−0.45z=−0.45  19.

The time it takes for Grade 11 students in a certain school to complete a physical fitness test is normally distributed with a mean of 15 minutes and a standard deviation of 4 minutes. If the students who get the fastest 10% completion times will be exempted from the additional gym workout sessions, what is the slowest time for a student to qualify for the exemption? (2 points)

A. 9.88 minutes           B.18.36 minutes          C.8.42 minutes          D.11.64 minutes        

20. Which of the following statements about the normal curve is FALSE?

A.The normal distribution is a continuous random probability distribution.

B. The standard normal distribution is unimodal. 

C. The total area under the normal distribution is one. 

D. All variables that are approximately normally distributed can be transformed into  normal variables.  21. Let z1=−1.80z1=−1.80 and  z2=−0.25z2=−0.25. Which among the following probabilities for z-score illustrates the area under the standard normal curve as shown at the right using  z1z1and z2z2 ?

A.P(−1.80<z<−0.25)P(−1.80<z<−0.25)  B.P(z>−0.25)P(z>−0.25)  C.P(−1.80>z<−0.25)P(−1.80>z<−0.25)  D.P(z>−1.80)P(z>−1.80)    22.Terence's scores in Mathematics this semester were rather inconsistent. His scores are as follows: 55, 100, 95, 85, 75, 100. How many scores are within one standard deviation of the mean? (2 points)
A.5     B.6     C.3     D.4 

23. Which is TRUE about the negative z- score?

A. A negative z-score means that the student’s score surpassed more than 50% of his classmates.
B. A negative z-score implies that the students scored higher than the class mean.

C. A negative z-score means that the student’s score is lower than the median. 
D. A negative z-score means that the student’s score is located at the right side of the curve. 

24. Find the area under the standard normal curve between z = 0 and z = – 1.05.
A. 0.1469

B. 0.4332 
C. 0.3531 
D.0.0668

18. Suppose that the vehicle speeds at an interstate location have a normal distribution with a mean equal to 70mph and a standard deviation equal to 8mph. What is the z-score for a speed of 68mph? (2 points)  
A.z=−0.35z=−0.35       B.z=−0.55z=−0.55       C.z=−0.25z=−0.25      D.z=−0.45z=−0.45 

19. The time it takes for Grade 11 students in a certain school to complete a physical fitness test is normally distributed with a mean of 15 minutes and a standard deviation of 4 minutes. If the students who get the fastest 10% completion times will be exempted from the additional gym workout sessions, what is the slowest time for a student to qualify for the exemption? (2 points)

A.9.88 minutes           B.18.36 minutes          C.8.42 minutes               D.11.64 minutes        

20. Which of the following statements about the normal curve is FALSE?

A. The normal distribution is a continuous random probability distribution.

B. The standard normal distribution is unimodal. 

C. The total area under the normal distribution is one. 

D. All variables that are approximately normally distributed can be transformed into  normal variables.  21. Let z1=−1.80z1=−1.80 and  z2=−0.25z2=−0.25. Which among the following probabilities for z-score illustrates the area under the standard normal curve as shown at the right using  z1z1and z2z2 ?

A. P(−1.80<z<−0.25)P(−1.80<z<−0.25)       B. P(z>−0.25)P(z>−0.25)       C. P(−1.80>z<−0.25)P(−1.80>z<−0.25)       D. P(z>−1.80)P(z>−1.80)  22.

Terence's scores in Mathematics this semester were rather inconsistent. His scores are as follows: 55, 100, 95, 85, 75, 100. How many scores are within one standard deviation of the mean? (2 points)

A.5      B.6      C.3      D.4 

23. Which is TRUE about the negative z- score?

A. A negative z-score means that the student’s score surpassed more than 50% of his classmates.

B. A negative z-score implies that the students scored higher than the class mean. 

C. A negative z-score means that the student’s score is lower than the median. 

D. A negative z-score means that the student’s score is located at the right side of the curve. 

24. Find the area under the standard normal curve between z = 0 and z = – 1.05.

A. 0.1469

B. 0.4332 

C. 0.3531 

D. 0.0668

A state university desires to accept only the top 10% of all graduating seniors who took their entrance test and are on the waiting list to those who belong in the next 10%. The scores in the test have a mean of 500 and a standard deviation of 100. Assume that the scores in the test are normally distributed.

15. Find the cutoff score for the test for those who will belong on the waiting list. 2 points

A. 600 

B. 640

C.800 

D. 584 

16. Find the cutoff score for the test for the top 10%. 2 points

A. 600    B. 628    C. 610    D. 584

17. What is the corresponding z score for the top 10% of all graduating seniors?

A. z=1.29z=1.29      B. z=−1.28z=−1.28      C. z=1.28z=1.28       D. z=−1.29

Choose the letter that best describes or answers the statement or question. Refer to the given problem for the following questions

The IQ scores of a large group of students are approximately normally distributed with a mean of 98 and a standard deviation of 12 

12. When a randomly chosen student from this group will have an IQ score whose corresponding z-score is positive; what is expected with the IQ score of the chosen student?

A. It is lower than the mean of 98.  

B. It is higher than the mean of 98. 

C. It is equal to the mean of 98. 

D. It is not equal to the mean of 98. 

13. The z-score of a random variable of a given distribution that is assumed to be normally distributed is 1.38. Which of the following is TRUE? 

I. The random variable corresponding to the given z-score is greater than the mean.

II. The random variable corresponding to the given z-score is 1.38 units away from the mean.

III. The probability of the random variable is 41.62%.

A. II only   B. I and II C. I only D I, II, and II 

14. What is the probability that a randomly chosen student will have an IQ score greater than 115? 2 points

A.0.0778        B.0.0793       C.0.922       D. 0.9207

6. What is the corresponding z-score that bounds the shaded area?
            z=

7. What is the area under the normal curve of the following situation?
       right of z=−1.43z=−1.43

8. What is the corresponding z-score that bounds the shaded area?
           z=

9. What is the area under the normal curve of the following situation?
         left of z=2.08z=2.08

10. What is the area under the normal curve of the following situation?
         between z=−0.87z=−0.87 and z=1.75z=1.75

11. What is the corresponding z-score that bounds the shaded area?
         z=

1. The total area under the normal curve is equal to

A.True    B.False

2. A standard normal curve is a normal probability distribution that has a mean of one and a standard deviation of one.
A.False     B.True

3. The normal distribution is a continuous curve and always has a positive value for f(X)f(X) .
A.True     B.False

4. The width of the curve in a normal distribution is determined by the standard deviation of the distribution.
A.False     B.True

5. The normal distribution is at its lowest point at the mean.
A.True     B.False

Hello when could we get started 

Ten (10) HUMSS students were selected from the respondents. Assuming 
that the population standard deviation of the GWA of HUMSS students is 3.6752. 
4. What is the probability that their average grade is below 88? (2 points)
      A. 0.3483         B. 0.409           C. 0.6064         D. 0.6517
5. What is the probability form that describes the probability of number 4?
      A. P(X<88)       B. P(X>88)       C. P(𝑋̅<88)       D. P(𝑋̅>88)

10. What is the best point estimate of the GWA of all senior high school students?
      A. 85 B. 87 C. 88 D. 89
11. At 99% confidence level, what is the confidence coefficient to be used?
      A. 1.282 B. 1.645 C. 1.96 D. 2.575
12. At 99% confidence level, what is the estimated standard error of the mean? (2 points)
      A. 0.2521 B. 0.2551 C. 0.2567 D. 0.2732
13. At 99% confidence level, what is the margin of error to estimate the GWA of all senior 
high school students? (2 points)
      A. 0.3291 B. 0.4223 C. 0.6610 D. 0.6613
14. At 99% confidence level, what is the interval estimate of the GWA of all senior high 
school students?
      A. 87.3556 - 88.6776 C. 87.5777 - 88.4223
      B. 87.4969 - 88.5031 D. 87.6709 - 88.3291
15. At 95% confidence level, what is the confidence coefficient to be used?
      A. 1.282 B. 1.645 C. 1.96 D. 2.576
16. At 95% confidence level, what is the estimated standard error? (2 points)
      A. 0.2521 B. 0.2551 C. 0.2567 D. 0.2732
17. At 95% confidence level, what is the margin of error to estimate the GWA of all senior 
high school students? (2 points)
      A. 0.3291 B. 0.4223 C. 0.5031 D. 0.6613
18. At 95% confidence level, what is the interval estimate of the GWA of all senior high 
school students?
      A. 87.3387 - 88.6613 C. 87.5777 - 88.4223
      B. 87.5135 - 88.5197 D. 87.6709 - 88.3291
For items 19-21, In preparation for the next school year, the school administrator wants to 
estimate the GWA. If they want to estimate the GWA accurate within an error of 0.75 from 
its true value,
19. What is the estimated population standard deviation?
      A. 2.93 B. 3.33 C. 3.43 D. 3.45
20. What should be the sample size at 99% confidence level? (2 points)
      A. 141 B. 200 D. 375 D. 425
21. What should be the sample size at 95% confidence level? (2 points)
      A. 65 B. 82 D. 92 D. 104

                            Students experience tremendous levels of stress throughout their education. A high level of stress may have a negative effect on the cognitive functioning and learning of students. The school administration of CSU - Laboratory High School - Senior High (CSU-LHS-SH) sought to determine the levels and primary sources of stress and its possible correlation with the General Weighted Average (GWA) in its department. As a statistician, your task is to conduct hypothesis testing to analyze the gathered data. Data were collected from students of CSU-LHS-SH during the first semester of the academic year 2021 - 2022.. The Student Stressor Questionnaire (SSQ) was used to collect the data.
            The SSQ contains 20 items that cover six subscales: (Academic-Related Stressors (ARS), Intrapersonal and Interpersonal Related Stressors (IRS), Learning-Related Stressors (LRS), Social-Related Stressors (SRS), Drive- and Desire-Related Stressors (DRS), and Group Activity-Related Stressors (GARS). Items in the SSQ represent 20 events that might be sources of stress (eg, “lack of time to review what has been learnt”, “heavy workload”). The responses were measured on a four-point Likert scale: “0=causing no stress”, “1=causing mild stress”, “2=causing high stress”, or “3=causing severe stress”.
            The findings of this study will contribute to the educational literature on the effect of stress on students’ academic performance, thus it must be accurate and timely.                                         No. STRAND MODALITY GWA ARS IRS LRS SRS DRS GARS                     1 ABM OBL 90 1 0 1 0 0 2 2 STEM OBL 90 2 0 2 1 0 1 3 STEM CBL 87 1 1 1 1 2 2 4 STEM OBL 90 1 0 1 0 1 1 5 STEM OBL 91 1 1 0 0 2 1 6 ABM CBL 90 1 0 1 1 0 1 7 STEM OBL 94 2 1 1 0 0 1 8 STEM OBL 93 2 0 2 1 0 1 9 ABM OBL 89 1 0 1 0 1 1 10 STEM CBL 87 2 2 1 1 2 2 11 ABM CBL 87 2 1 1 1 1 2 12 ABM OBL 89 2 0 1 0 0 2 13 ABM OBL 89 1 0 1 2 1 1 14 ABM CBL 83 3 2 3 2 3 3 15 STEM OBL 95 0 0 0 0 0 1 16 HUMSS OBL 90 1 0 1 1 0 1 17 HUMSS OBL 89 1 1 1 0 0 3 18 HUMSS OBL 89 1 0 1 1 1 1 19 STEM OBL 89 0 0 1 1 2 2 20 HUMSS CBL 90 1 0 1 2 0 1 21 HUMSS OBL 92 0 0 0 0 1 2 22 HUMSS CBL 84 3 2 2 1 3 2 23 HUMSS CBL 86 2 2 2 2 2 2 24 HUMSS OBL 90 1 0 1 0 1 1 25 STEM CBL 93 1 0 0 0 0 2 26 STEM CBL 95 1 0 1 0 1 2 27 STEM CBL 87 3 1 3 1 2 1 28 STEM OBL 94 0 1 0 1 0 0 29 HUMSS OBL 85 3 1 2 2 2 3 30 STEM OBL 88 2 0 1 0 1 3 31 ABM CBL 80 3 2 3 3 3 3 32 STEM OBL 88 3 0 1 0 1 2 33 HUMSS CBL 83 3 2 3 2 3 2 34 STEM OBL 88 2 1 1 1 1 2 35 ABM OBL 88 2 0 1 0 1 2 36 STEM CBL 85 3 1 3 2 2 2 37 STEM CBL 80 3 3 3 3 3 3 38 STEM CBL 82 3 3 3 2 3 3 39 STEM OBL 87 3 1 1 1 3 2 40 STEM OBL 88 2 0 1 0 0 2 41 STEM CBL 86 1 1 1 2 2 2 42 STEM OBL 92 1 1 0 1 0 1 43 HUMSS CBL 87 2 2 1 0 2 3 44 ABM OBL 90 2 1 0 0 1 1 45 STEM OBL 93 0 1 0 0 1 1 46 STEM OBL 92 1 1 0 0 0 2 47 STEM CBL 84 2 2 2 2 3 3 48 STEM CBL 84 3 3 2 2 3 3 49 ABM OBL 85 3 1 2 2 2 2 50 ABM CBL 86 2 1 1 2 2 2 51 STEM OBL 91 0 0 1 0 0 3 52 HUMSS CBL 82 3 3 3 3 3 3 53 HUMSS CBL 80 3 3 3 3 3 3 54 ABM OBL 85 3 1 2 2 2 2 55 STEM OBL 88 2 0 2 0 1 1 56 STEM OBL 87 2 1 1 1 2 1 57 STEM CBL 84 3 2 3 3 2 2 58 STEM OBL 91 1 0 0 1 0 3 59 ABM CBL 81 3 3 3 2 2 3 60 ABM OBL 90 1 0 1 0 0 1 61 ABM OBL 87 2 1 1 0 2 2 62 ABM OBL 87 2 1 1 1 2 2 63 STEM OBL 85 3 1 2 2 2 2 64 STEM OBL 86 2 1 1 2 2 2 65 ABM OBL 86 2 1 3 2 2 2 66 ABM OBL 93 0 0 1 0 0 1 67 STEM CBL 87 2 0 1 1 2 2 68 STEM OBL 88 1 2 1 2 1 3 69 ABM OBL 89 0 1 2 0 0 1 70 ABM OBL 89 1 0 1 0 1 1 71 STEM OBL 91 2 0 2 0 0 1 72 STEM CBL 85 1 1 2 2 2 3 73 HUMSS OBL 93 1 0 2 0 0 1 74 STEM CBL 89 1 0 1 0 1 2 75 STEM OBL 86 2 1 1 2 2 2 76 STEM OBL 85 3 1 3 2 2 3 77 HUMSS OBL 85 2 1 2 2 3 2 78 STEM OBL 91 1 0 0 0 1 1 79 STEM OBL 86 2 1 1 2 2 2 80 STEM CBL 83 2 1 3 2 3 3 81 STEM OBL 94 0 1 0 0 0 1 82 ABM CBL 82 3 2 3 2 3 3 83 STEM OBL 89 1 1 1 0 1 1 84 ABM OBL 86 2 2 1 1 2 2 85 STEM OBL 87 2 1 2 0 2 2 86 STEM CBL 83 3 2 3 2 3 3 87 STEM OBL 85 2 1 2 2 2 2 88 STEM OBL 88 2 0 1 0 1 2 89 STEM CBL 85 3 2 2 2 2 2 90 STEM OBL 88 2 0 1 0 1 2 91 ABM OBL 94 0 1 0 1 0 1 92 ABM OBL 85 3 0 1 2 2 2 93 ABM CBL 88 2 0 2 0 1 2 94 STEM CBL 86 2 1 1 2 2 2 95 STEM OBL 85 3 2 2 1 3 2 96 STEM OBL 86 2 2 1 2 2 2 97 STEM OBL 85 3 1 2 2 2 2 98 STEM OBL 92 1 0 1 0 0 2 99 ABM CBL 90 0 1 2 0 1 3 100 STEM CBL 81 3 3 3 2 3 3 101 HUMSS OBL 89 1 0 2 0 1 1 102 STEM CBL 88 3 0 1 0 1 0 103 HUMSS CBL 85 3 2 3 2 2 2 104 STEM OBL 89 0 0 2 0 1 1 105 STEM OBL 87 2 2 1 1 1 3 106 STEM OBL 89 1 0 1 1 1 1 107 STEM OBL 95 1 0 0 0 1 0 108 HUMSS CBL 84 3 2 2 2 3 3 109 STEM CBL 81 3 3 3 2 2 1 110 STEM OBL 86 2 1 0 2 2 3 111 STEM OBL 89 1 1 1 0 1 1 112 STEM OBL 91 1 0 0 0 0 1 113 STEM OBL 91 1 1 0 0 0 1 114 STEM CBL 89 1 1 0 0 1 1 115 STEM CBL 83 3 2 3 2 3 3 116 STEM OBL 91 3 0 0 0 0 1 117 STEM OBL 95 1 0 1 0 0 1 118 STEM OBL 87 1 1 1 2 2 2 119 STEM OBL 87 2 1 1 1 2 2 120 STEM OBL 89 0 0 1 0 1 3 121 STEM OBL 88 1 0 0 1 1 2 122 STEM OBL 91 1 0 0 1 0 2 123 STEM OBL 92 0 0 0 1 0 3 124 ABM CBL 84 3 2 2 2 3 3 125 STEM OBL 84 3 3 2 2 3 3 126 STEM CBL 83 3 1 3 2 3 3 127 STEM CBL 88 2 0 1 0 1 2 128 STEM OBL 92 1 0 0 1 1 2 129 STEM OBL 85 3 1 2 2 2 2 130 STEM CBL 87 2 1 0 1 2 2 131 STEM OBL 91 0 0 2 0 1 1 132 STEM OBL 88 2 1 0 0 1 3 133 STEM OBL 89 1 0 1 0 1 1 134 STEM CBL 88 2 2 1 2 1 2 135 STEM CBL 82 3 2 3 3 3 3 136 STEM OBL 88 2 0 1 0 1 2 137 HUMSS OBL 89 1 0 1 0 1 2 138 STEM OBL 92 1 0 0 0 0 1 139 ABM OBL 92 0 1 1 0 0 1 140 STEM OBL 92 0 0 1 0 1 1 141 ABM OBL 84 3 2 2 2 3 3 142 ABM OBL 88 1 0 2 0 0 3 143 HUMSS OBL 88 2 1 1 1 1 1 144 STEM OBL 90 1 0 1 0 0 1 145 HUMSS OBL 90 0 1 1 0 0 2 146 HUMSS OBL 90 1 0 1 0 0 1 147 STEM OBL 89 1 0 1 0 1 1 148 HUMSS OBL 94 0 0 0 1 0 2 149 STEM OBL 86 2 1 1 2 2 2 150 STEM OBL 90 0 1 1 0 1 2 151 ABM OBL 86 3 1 1 2 2 2 152 STEM OBL 86 3 1 1 2 2 2 153 STEM OBL 92 0 1 0 0 0 2 154 STEM OBL 90 1 0 2 1 0 1 155 STEM OBL 92 1 1 1 1 1 1 156 HUMSS OBL 86 3 1 2 2 2 3 157 STEM OBL 93 1 0 1 0 0 2 158 ABM OBL 86 2 1 1 2 2 2 159 ABM OBL 91 2 2 0 0 0 1 160 ABM OBL 93 2 0 1 0 0 1 161 ABM OBL 87 1 1 1 2 1 3 162 ABM OBL 87 2 0 1 1 2 2 163 ABM OBL 95 0 1 1 0 0 2 164 ABM OBL 86 2 1 1 2 2 2 165 STEM OBL 91 1 0 0 0 0 1 166 ABM OBL 87 2 1 1 1 2 1 167 ABM OBL 88 2 0 1 0 1 2 168 ABM OBL 93 0 1 0 1 0 2 169 HUMSS OBL 87 2 1 0 1 2 2 170 HUMSS OBL 84 3 2 2 2 3 3 171 HUMSS OBL 93 1 1 0 0 0 1 172 STEM OBL 84 3 2 2 2 3 3 173 STEM OBL 92 1 1 0 0 0 2 174 ABM OBL 83 3 2 3 2 3 3 175 HUMSS OBL 94 1 0 0 0 1 1 176 ABM OBL 91 1 0 1 0 0 1 177 HUMSS OBL 85 3 1 2 1 2 2 178 ABM OBL 86 2 1 1 2 1 2 179 STEM OBL 90 1 0 1 0 2 2 180 STEM OBL 84 3 2 2 1 3 3 181 STEM OBL 88 2 0 1 1 2 2

10. What is the best point estimate of the GWA of all senior high school students?
      A. 85 B. 87 C. 88 D. 89
11. At 99% confidence level, what is the confidence coefficient to be used?
      A. 1.282 B. 1.645 C. 1.96 D. 2.575
12. At 99% confidence level, what is the estimated standard error of the mean? (2 points)
      A. 0.2521 B. 0.2551 C. 0.2567 D. 0.2732
13. At 99% confidence level, what is the margin of error to estimate the GWA of all senior 
high school students? (2 points)
      A. 0.3291 B. 0.4223 C. 0.6610 D. 0.6613
14. At 99% confidence level, what is the interval estimate of the GWA of all senior high 
school students?
      A. 87.3556 - 88.6776 C. 87.5777 - 88.4223
      B. 87.4969 - 88.5031 D. 87.6709 - 88.3291
15. At 95% confidence level, what is the confidence coefficient to be used?
      A. 1.282 B. 1.645 C. 1.96 D. 2.576
16. At 95% confidence level, what is the estimated standard error? (2 points)
      A. 0.2521 B. 0.2551 C. 0.2567 D. 0.2732
17. At 95% confidence level, what is the margin of error to estimate the GWA of all senior 
high school students? (2 points)
      A. 0.3291 B. 0.4223 C. 0.5031 D. 0.6613
18. At 95% confidence level, what is the interval estimate of the GWA of all senior high 
school students?
      A. 87.3387 - 88.6613 C. 87.5777 - 88.4223
      B. 87.5135 - 88.5197 D. 87.6709 - 88.3291
For items 19-21, In preparation for the next school year, the school administrator wants to 
estimate the GWA. If they want to estimate the GWA accurate within an error of 0.75 from 
its true value,
19. What is the estimated population standard deviation?
      A. 2.93 B. 3.33 C. 3.43 D. 3.45
20. What should be the sample size at 99% confidence level? (2 points)
      A. 141 B. 200 D. 375 D. 425
21. What should be the sample size at 95% confidence level? (2 points)
      A. 65 B. 82 D. 92 D. 104