Given:
Mean, μ = 22
Standard deviation, σ = 7
Let's answer the following questions.
a. Given:
Sample size, n = 25
Let's find the probability that the sample mean is between 21.5 and 22.5.
We have:
Therefore, the probability that sample mean is between 21.5 and 22.5 is 0.279
b. Given:
n = 25
Let's find the probability that the sample mean is between 21 and 22 minutes.
We have:
[tex]\begin{gathered} P(21Using the standard normal table, we have:[tex]\begin{gathered} P(-0.714286Therefore, the probability that sample mean is between 21 and 22 is 0.2625c. Given:
n = 144
Let's find the probability the sample mean is between 21.5 and 22.5
[tex]\begin{gathered} P(21.5Therefore, the probability that sample mean is between 21.5 and 22.5 given a sample of 144 is 0.6086d. Given:
Sample size in a = 25
Sample size in c = 144
The sample size in c is greater than the sample size in a so the standard error of the mean in (c) should be less than the standard error in (a).
As the standard error values become more concentrated