Thirty randomly selected students took the calculus final. If the sample mean was 89 and the standard deviation was 6.2, construct a 99% confidence interval of the mean score of all students. Assume that the population has a normal distribution.

what formula do i use????

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.005) and its Z score.

99% = mean ± Z SEm

SEm = SD/√n

To construct a confidence interval for the mean score of all students, we can use the formula:

CI = x̄ ± Z * (σ/√n)

Where:
CI is the confidence interval
x̄ is the sample mean
Z is the z-value corresponding to the desired level of confidence
σ is the population standard deviation
n is the sample size

In this case, we are given:
Sample mean (x̄) = 89
Standard deviation (σ) = 6.2
Sample size (n) = 30
Level of confidence = 99%

To find the z-value corresponding to the 99% confidence level, we can use a table or calculate it using statistical software. The z-value for a 99% confidence level (two-tailed) is approximately 2.576.

Plugging the given values into the formula, we have:

CI = 89 ± 2.576 * (6.2/√30)

Now, we can calculate the confidence interval:

CI = 89 ± (2.576 * 1.131)

CI = 89 ± 2.92

Therefore, the 99% confidence interval for the mean score of all students is [86.08, 91.92].

To construct a confidence interval for the mean score of all students, you will use the formula for a confidence interval of a population mean. The formula is:

Confidence Interval = sample mean ± (critical value \* (standard deviation / square root of sample size))

In this case, you are looking for a 99% confidence interval. Since you assume that the population has a normal distribution, you can use the Z-distribution and find the critical value associated with a 99% confidence level.

The critical value corresponds to the level of confidence you desire and is based on the Z-score or the Standard Normal Distribution. For a 99% confidence level, the critical value is found by looking up the Z-score for (1 - 0.99) / 2 = 0.005 in the Z-table.

Once you have the critical value, you can substitute it, along with the given sample mean (89), standard deviation (6.2), and sample size (30), into the formula to calculate the confidence interval.