Question

a population is known to be normally distributed. a random sample of size 15 is taken. the sample mean is 75 and the sample standard deviation is 5. find the right end point of a symmetric 95% confidence interval for the population mean pe

Answer 1

The right end point of the 95% confidence interval is approximately 78.19.

Step-by-step explanation:

To find the right end point of a symmetric 95% confidence interval for the population mean, we can use the formula: right end point = sample mean + (Z * standard deviation/square root of sample size), where Z is the z-score corresponding to the desired confidence level. In this case, since the confidence level is 95%, Z is the z-score corresponding to a cumulative probability of 0.975.

First, we look up the z-score for a cumulative probability of 0.975, which is approximately 1.96. Then, we plug in the given values: sample mean = 75, standard deviation = 5, and sample size = 15, into the formula.

Thus, the right end point of the 95% confidence interval for the population mean is 75 + (1.96 * 5/√15) = 75 + (1.96 * 5/3.87) ≈ 75 + 3.19 ≈ 78.19.