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A random sample is drawn from a population with mean μ = 53 and standard deviation...

A random sample is drawn from a population with mean μ = 53 and standard deviation σ = 4.4. [You may find it useful to reference the z table.]

a. Is the sampling distribution of the sample mean with n = 13 and n = 38 normally distributed?

  • Yes, both the sample means will have a normal distribution.

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

  • No, only the sample mean with n = 13 will have a normal distribution.

  • No, only the sample mean with n = 38 will have a normal distribution.

b. Calculate the probability that the sample mean falls between 53 and 55 for n = 38. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

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