The amount of material used in making a custom sail for a sailboat is normally distributed with a standard deviation of 64 square feet. For a random sample of 15 sails, the mean amount of material used is 912 square feet. Which of the following represents a 99% confidence interval for the population mean amount of material used in a custom sail? A. 912 ± 49.2B. 912 ± 46.8C. 912 ± 42.6D. 912 ± 44.3

option (B) 912 ± 42.6

Explanation:

Data provided in the question:

Standard deviation = 64 square feet

Sample size, n = 15

Mean = 912

Confidence level = 99%

Now,

Confidence interval = Mean ± z[s : √n]

here,

z = 2.58 for 99% confidence level

Thus,

Confidence interval = 912 ± 2.58[64 : √15]

or

Confidence interval = 912 ± 2.58[64 : √15]

or

Confidence interval = 912 ± [ 2.58 * 16.525 ]

or

Confidence interval = 912 ± 42.63

= 912 ± 42.6

Hence,

The answer is option (B) 912 ± 42.6