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CH-HW4-Sampling-Distribution: Problem 1 R euser CH-Emil-38effectiveUser=t-Emil3 Previous Problem Problem List Next Problem (3 points) The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with a mean 530.2 and a standard deviation of 29.2 (a) What is the probability that a single student randomly chosen from all those taking the test scores 536 or higher? Probability = (Expressing the probability as a proportion and rounding it to 4 decimal places) For parts (b) through (c), consider a random sample of 30 students who took the test. (b) What are the mean and standard deviation of the sample mean score X, of 30 students? The mean of the sampling distribution for X is: The standard deviation of the sampling distribution for X is: (Rounding the standard deviation to 6 decimal places) (c) What is the probability that the mean score X of these students is 536 or higher? Probability = (Expressing the probability as a proportion and rounding it to 4 decimal places) Note: You can earn partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0 times You have 3 attempts remaining

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

The scores of individual students on the American College Testing (ACT) composite college entrance examination have a Normal distribution with mean 18.6 and standard deviation 5.9. What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?

Use the following scenario for questions 6 – 8. In 2016-17, the average SAT score of the UVA first year class was 1420 out of 1600. An advisor in the statistics department is interested in determining whether statistics majors from that class have higher SAT scores than the average. He tests H,:Β΅ = 1420 against HαΊ‘: Β΅ > 1420, where u is the mean SAT score for statistics majors from the 2016-17 first year class. In a simple random sample of 30 statistics majors, he finds a sample mean SAT score of 1440 with sample standard deviation of 40.

6. What is the value of the test statistic for this significance test?

a. 0.09

b. 0.5

c. 2.73

d. 20

7. From what distribution is this test statistic?

a. N(0, 1)

b. N(1420, 7.30)

c. t distribution with 29 degrees of freedom

d. t distribution with 28 degrees of freedom

8.) The p-value for this test is 0.005. Which of the following is a proper interpretation of this p- value?

a.There is a 0.5% chance that the null hypothesis is true.

b. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample a. mean SAT score from 30 statistics majors would equal 1440.

c.If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or lower.

d. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or higher.

"Time headway" in traffic flow................

"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X=the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form.

Β 

(a) Determine the value of k for which f(x) is a legitimate pdf.

(b) Obtain the cumulative distribution function.

(c) Use the cdf from (b) to determine the probability that headway exceeds 2sec. (Round your answer to three decimal places).

(d) Obtain the mean value of headway and the standard deviation of headway.(Round your answers to three decimal places).

(e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answr to three decimal places).

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