At a particular academically challenging high school,the average GPA of a high school senior is known to be normally distributed.After a sample of 20 seniors is taken,the average GPA is found to be 2.71 and the variance is determined to be 0.25.Find a 90% confidence interval for the population mean GPA.
A)[2.5167,2.9033]
B)[2.5261,2.3939]
C)[2.5615,2.8585]
D)[2.6358,2.7842]

Question

Quizplus · Accepted Answer

The correct answer is A because the 90% confidence interval for the population mean GPA is (2.5167, 2.9033). This interval was calculated using the formula:CI = x̄ ± z * (s / √n)where x̄ is the sample mean, z is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.In this case, x̄ = 2.71, s = 0.5, n = 20, and the 90% confidence level corresponds to a z-score of 1.645. Plugging these values into the formula, we get:CI = 2.71 ± 1.645 * (0.5 / √20)CI = 2.71 ± 0.1934CI = (2.5167, 2.9033)

At a Particular Academically Challenging High School,the Average GPA of a High