A Statistics class is estimating the mean height of all female students at their college. They collect a random sample of 36 female students and measure their heights. The mean of the sample is 65.3 inches. The standard deviation is 5.2 inches. Use the T-distribution Inverse Calculator applet to answer the following question. What is the 90% confidence interval for the mean height of all female students in their school?

a. (56.5, 74.1)

b. (63.6, 67.0)

c. (63.8, 66.8)

d. (63.9, 66.7)

d. (63.9, 66.7)

Therefore at 90% confidence interval (a, b) = (63.9, 66.7)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 65.3

Standard deviation r = 5.2

Number of samples n = 36

Confidence interval = 90%

z (at 90% confidence) = 1.645

Substituting the values we have;

65.3+/-1.645 (5.2/√36)

65.3+/-1.645 (0.866667)

65.3+/-1.42567

65.3+/-1.4

= (63.9, 66.7)

Therefore at 90% confidence interval (a, b) = (63.9, 66.7)