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A random sample is drawn from a normally distributed population with mean μ = 23 and...

A random sample is drawn from a normally distributed population with mean μ = 23 and standard deviation σ = 2.6. [You may find it useful to reference the z table.]

a. Are the sampling distribution of the sample mean with n = 31 and n = 62 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 = 31 will have a normal distribution.

  • No, only the sample mean with n = 62 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 23.7 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.)

Solutions

Expert Solution

a) Option-A) Yes, both the sample means will have a normal distribution.

b)

                                

                                 = P(Z < 1.50)

                                 = 0.9332

n = 62

                             

                              = P(Z < 2.12)

                              = 0.9830

milcah answered 2 months ago
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