A study of 60 bolts of carpet showed that their average length was 180 yards. The standard deviation of the population is 6 yards. Which of the following is the 99% confidence interval for the mean length per bolt of carpet?

No alternatives given. Cannot copy and paste here.

99% = mean ± 2.575 SEm

SEm = SD/√n

You do the math.

To find the 99% confidence interval for the mean length per bolt of carpet, we can use the formula:

Confidence interval = sample mean +/- (critical value * standard deviation / square root of sample size)

First, let's determine the critical value. Since we have a sample size of 60 and want a 99% confidence level, we will use a z-score.

The critical value for a 99% confidence level can be found using a standard normal distribution table or a calculator. In this case, the critical value is approximately 2.61.

Next, we plug the values into the formula:

Confidence interval = 180 +/- (2.61 * 6 / √60)

Calculating this expression, we get:

Confidence interval = 180 +/- (15.66 / 7.75)

Simplifying the expression, we get:

Confidence interval = 180 +/- 2.02

Therefore, the 99% confidence interval for the mean length per bolt of carpet is approximately (177.98, 182.02) yards.

To find the 99% confidence interval for the mean length per bolt of carpet, we can use the formula:

Confidence Interval = Mean ± (Z-score * Standard Deviation / √n)

Where:
- Mean is the average length of the bolts of carpet (180 yards).
- Z-score is the critical value corresponding to the desired confidence level. For a 99% confidence level, the critical value is 2.576.
- Standard Deviation is the standard deviation of the population (6 yards).
- n is the sample size (60 bolts of carpet).

Substituting the values into the formula, we get:

Confidence Interval = 180 ± (2.576 * 6 / √60)

Calculating the expression inside the parentheses:
2.576 * 6 = 15.456

Calculating the square root of the sample size:
√60 ≈ 7.746

Now, divide the expression by the square root of the sample size:
15.456 / 7.746 ≈ 1.994

The confidence interval is therefore:
180 ± 1.994

To calculate the upper and lower bounds of the confidence interval, we add and subtract 1.994 from the mean:

Lower bound: 180 - 1.994 ≈ 178.006
Upper bound: 180 + 1.994 ≈ 181.994

Therefore, the 99% confidence interval for the mean length per bolt of carpet is approximately 178.006 to 181.994 yards.