A continuous population has a mean of 210.51 and a standard deviation of 10.31.Suppose we know that the population is normally distributed.Compute the smallest interval centered on the mean that will contain 95% of the observations.
A) (200.20, 220.82)
B) (164.40, 256.62)
C) (179.58, 241.44)
D) (189.89, 231.13)

Question

Quizplus · Accepted Answer

A 95% confidence interval centered on the mean would encompass 47.5% on either side. Using a standard normal distribution table, we can find the z-score corresponding to the 0.475 percentile, which is approximately 1.96. Then, we can use the formula:
(mean - z*(standard deviation)/sqrt(sample size), mean + z*(standard deviation)/sqrt(sample size))
where the sample size is assumed to be large enough that we can use the population standard deviation as an estimate. Plugging in the values, we get:
(210.51 - 1.96*(10.31)/sqrt(infinity), 210.51 + 1.96*(10.31)/sqrt(infinity))
which simplifies to:
(189.89, 231.13)
Therefore, D is the correct choice.

A Continuous Population Has a Mean of 210