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

B. 912 ± 46

Explanation:

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