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

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season

The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated?

a.Compute the theoretical mean of the random variable X for the given probability distribution.

Meu = ?

b. Compute the theoretical standard deviation of the random variable X for the given probability distribution.

Sigma =?

c.Approximate the mean of the random variable X based on the simulation for 25 games.

Xbar=?

d. Approximate the standard deviation of the random variable X based on the simulation for 25 games.

S=?

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season x P(x) 0 0.167 1 0.3289 2 0.2801 3 0.149 4 0.0382 5 0.0368 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated? a.Compute the theoretical mean of the random variable X for the given probability distribution. Meu = ? b. Compute the theoretical standard deviation of the random variable X for the given probability distribution. Sigma =? c.Approximate the mean of the random variable X based on the simulation for 25 games. Xbar=? d. Approximate the standard deviation of the random variable X based on the simulation for 25 games. S=?

If x is a random variable with a normal distribution (335, 50), find the z-score corresponding to an observation of 284.

A  Compute and interpret the mean of the random variable x

B Compute the standard deviation of the random variable x.

C. What is the probability that a randomly selected student has a parent involved in three activities?

D  What is the probability that a randomly selected student has a parent involved in three or four activities?

E.

In the following probability distribution, the random variable x represents the number of activities a K to the 5th-grade student is involved in.

Complete parts (a) through (f) below.

   x           0              1               2               3               4

P(x)      0.299       0.145         0.234        0.053         0.269

(a) Verify that this a discrete probability distribution.