Question

A study of 65 bolts of carpet showed that their average length was 74.2 yards. The standard deviation of the population is 3.6 yards. Which of the following is the 98% confidence interval for the mean length per bolt of carpet?

A) 73.8 μ 75.6
B) 72.6 μ 76.8
C) 73.2 μ 75.2
D) 74.6 μ 75.8

Answer 1

To calculate the 98% confidence interval for the mean length per bolt of carpet, we can use the formula: CI = X ± Z(σ/√n). First, find the Z-score for the 98% confidence level. Then, substitute the values into the formula and simplify to find the confidence interval.

Step-by-step explanation:

To calculate the 98% confidence interval for the mean length per bolt of carpet, we can use the formula: CI = X ± Z(σ/√n)

Where:

• CI is the confidence interval
• X is the sample mean (74.2 yards)
• Z is the Z-score corresponding to the desired confidence level (98%)
• σ is the population standard deviation (3.6 yards)
• n is the sample size (65)

First, we need to find the Z-score for the 98% confidence level. Looking up the Z-score in a Z-table, we find that the Z-score is approximately 2.33.

Then, we can substitute the values into the formula:

CI = 74.2 ± 2.33 * (3.6/√65)

Simplifying the formula, we get:

CI = 74.2 ± 0.461

Therefore, the 98% confidence interval for the mean length per bolt of carpet is (73.8, 74.6) yards.