Question

Descriptive analysis revealed that the mean Test 3 score of all 63 students in Dr. Kilman’s statistics courses was an 80. Similarly, the standard deviation for all students’ Test 3 scores was found to be 16. Assume the Test 3 scores are approximately normally distributed. Next, suppose a random sample of 36 students is drawn. Let  be the mean Test 3 score of such a sample.

12. Since the standard deviation of the sampling distribution () is ______ than the population standard deviation (), the sampling distribution curve will be ________ than the population distribution curve.  

13. What is the probability that the mean score of a random sample of 36 Test 3 scores is a 75 or higher? That is, calculate . Round your solution to four decimal places.

Answer 1

12)

Since the standard deviation of the sampling distribution () is less than the population standard deviation(), the sampling distribution curve will be narrower than the population distribution curve.

13) P( > 75)

= P(Z > -1.875)

= 1 - P(Z < -1.875)

= 1 - 0.0304

= 0.9696