Question

Efficient manufacturing: Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 75 clamps, the mean time to complete this step was 56.8 seconds. Assume that the population standard deviation is =σ  10 seconds. Round the critical value to no less than three decimal places.

(a) Construct a 99% confidence interval for the mean time needed to complete this step. Round the answer to at least one decimal place.

Answer 1

Solution :

Given that,

Sample size = n = 75

Z/2 = 2.576

Margin of error = E = Z/2* ( /n)

= 2.576 * (10 / 75)

Margin of error = E = 3.0

At 99% confidence interval estimate of the population mean is,

- E < < + E

56.8 - 3.0 < < 56.8 + 3.0

53.8 < < 59.8

( 53.8,59.8)

99% confidence interval for the mean is

( 53.8 , 59.8 )