Question

The heights in inches of orangutans Are normally distributed with a population standard deviation of 3" and an unknown population mean if a random sample of 17 orangutans is taken and results in a sample mean of 57" find the error bound of the confidence interval with a 95% confidence level

Answer 1

Answer: The 95% confidence interval is approximately (55.57, 58.43)

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Explanation:

At 95% confidence, the z critical value is about z = 1.960 which you find using a table or a calculator.

The sample size is n = 17

The sample mean is xbar = 57

The population standard deviation is sigma = 3

The lower bound of the confidence interval is

L = xbar - z*sigma/sqrt(n)

L = 57 - 1.960*3/sqrt(17)

L = 55.5738905247863

L = 55.57

The upper bound is

U = xbar + z*sigma/sqrt(n)

U = 57 + 1.960*3/sqrt(17)

U = 58.4261094752137

U = 58.43

Therefore the confidence interval (L, U) turns into (55.57, 58.43) which is approximate.