A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice.The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35.Construct a 99% confidence interval for the average number of free throws in practice.
A) [210.5995,239.4005]
B) [210.6155,239.3845]
C) [211.2506,238.7494]
D) [214.2290,235.7710]

Question

Quizplus · Accepted Answer

Using the formula for a confidence interval for the population mean:
CI = X̄ ± Zα/2 (σ/√n)

X̄ = 225 (sample mean)
σ = 35 (population standard deviation)
n = 43 (sample size)
Zα/2 = 2.576 (from a z-table for a 99% confidence level)

Plugging in the values:
CI = 225 ± 2.576(35/√43)
CI = 225 ± 10.4
CI = [210.6, 239.4]

Therefore, the best choice is A, as it corresponds to the calculated confidence interval.

A Basketball Coach Wants to Know How Many Free Throws