Question

In Colorado, the average ACT score is 20.1 with a standard deviation of 1.3. We collect a random sample of 35 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 19.5 or less? 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 = = 20.1

standard deviation = = 1.3

n = 35.

Yes.

=   20.1

= / n = 1.3 / 35 = 0.2197 = 0.22

P( ≤ 19.5 ) = P(( - ) / ≤ (19.5 - 20.1) /0.22 )

= P(z ≤ -2.727)

= 0.0032

probability =0.0032