Question

Asked Oct 24, 2019

Give a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample of:

- 4 has a mean between 49 and 52
- 16 has a mean between 49 and 52
- 25 has a mean between 49 and 52

Please do not solve using Microsoft Excel because my professor is not teaching using excel and I would like to see the steps involved in solving the equation.

Step 1

1.

The probability that random sample of 4 has a mean between 49 and 52 is obtained below:

From the information, by central limit theorem for mean, follows a normal distribution with mean μ = 50 and standard deviation, 5 /sqrt (4) = 2.5.

Step 2

2.

The probability that random sample of 16 has a mean between 49 and 52 is obtained below:

From the information, by central limit theorem for mean, follows a normal distribution with mean μ = 50 and standard deviation, 5 /sqrt (16) =1.25.

Step 3

3.

The probability that random sample of 25 has a mean between 49 and 52 is obtained below:

From the information, by central li...

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