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Question: a random sample is drawn from a normally distributed population...

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A random sample is drawn from a normally distributed population with mean μ = 22 and standard deviation σ = 1.9. [You may find it useful to reference the z table.]

a. Are the sampling distribution of the sample mean with n = 30 and n = 60 normally distributed?

  • Yes, both the sample means will have a normal distribution. X (this is the correct answer)

  • No, both the sample means will not have a normal distribution.

  • No, only the sample mean with n = 30 will have a normal distribution.

  • No, only the sample mean with n = 60 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 22.9 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

   N Probability
30 =
60 =

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