Question

In Nebraska, the average ACT score is 21.7 with a standard deviation of 1.1. We collect a random sample of 30 students who took the exam last year.

Part 1: (6 pts)

Check the all necessary conditions in detail (not just yes or no) (1 pt each) and give the sampling model and parameters to 2 decimal places (2 pts).

Part 2: (8 pts)

What is the probability that the average composite ACT score is 22.1 or more? Show your calculations for finding the z-score to three decimal places (4 pts), then find the probability to four decimal places using the appropriate probability notation (2 pts). Write a sentence that gives your solution in context (2 pts).

Answer 1

Solution :

Given that ,

mean = = 21.7

standard deviation = = 1.1

n = 30

Part 1

= 21.7 and

= / n = 1.1 / 30 = 0.2008

Part 2

P( 22.1) = 1 - P( 22.1)

= 1 - P(( - ) / (22.1 - 21.7) / 0.2008)

= 1 - P(z 1.992)

= 1 - 0.9768

= 0.0232

Probability = 0.0232

The probability that the average composite ACT score is 22.1 or more is 0.0232 .