According to a study of 90 truckers, a trucker drives, on average, 540 miles per day. If the standard deviation of the miles driven per day for the population of truckers is 40, find the 99% confidence interval of the mean number of miles driven per day by all truckers.

To find the 99% confidence interval of the mean number of miles driven per day by all truckers, we will use the formula:

Confidence Interval = Sample Mean ± (Z * Standard Error)

First, we need to find the standard error, which is the standard deviation of the sample mean. The formula for calculating the standard error is:

Standard Error = Standard Deviation / √(Sample Size)

Given that the sample size is 90 and the standard deviation is 40, we can calculate the standard error as follows:

Standard Error = 40 / √(90)

Next, we need to find the value of Z, which is the z-score corresponding to the 99% confidence level. The z-score represents the number of standard deviations away from the mean.

For a 99% confidence level, we need to find the z-value where the area to the right is 0.5% or 0.005. Looking up this value in a standard normal distribution table, we find that the z-value is approximately 2.576.

Now we can calculate the confidence interval using the formula:

Confidence Interval = Sample Mean ± (Z * Standard Error)

Sample Mean = 540
Z = 2.576
Standard Error = 40 / √(90)

Confidence Interval = 540 ± (2.576 * (40 / √(90)))

Calculating this expression will give us the 99% confidence interval for the mean number of miles driven per day by all truckers.

To find the 99% confidence interval of the mean number of miles driven per day by all truckers, we can use the formula:

Confidence Interval = Sample Mean ± (Z * Standard Error)

First, we need to find the standard error, which is the standard deviation of the sample divided by the square root of the sample size. In this case, the sample size is 90 and the standard deviation is 40. So, the standard error is:

Standard Error = Standard Deviation / √Sample Size

Standard Error = 40 / √90 = 4.21 (rounded to two decimal places)

Next, we need to find the Z-score for a 99% confidence level. The Z-score corresponds to the area under the normal distribution curve that contains 99% of the data. The Z-score can be obtained from a Z-table or calculated using statistical software. For a 99% confidence level, the Z-score is approximately 2.576.

Lastly, we can calculate the confidence interval using the formula:

Confidence Interval = Sample Mean ± (Z * Standard Error)

Confidence Interval = 540 ± (2.576 * 4.21)

Now we can compute the lower and upper bounds of the confidence interval:

Lower Bound = 540 - (2.576 * 4.21) ≈ 528.32 (rounded to two decimal places)
Upper Bound = 540 + (2.576 * 4.21) ≈ 551.68 (rounded to two decimal places)

Therefore, the 99% confidence interval of the mean number of miles driven per day by all truckers is approximately 528.32 to 551.68 miles.

You need to find SD that includes ± 49.5% (.495) of the cases from the mean on both sides (.495 + .495 = .99).

99% confidence interval = mean ± 2.585 SD