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A random sample is drawn from a normally distributed population with mean μ = 30 and...

A random sample is drawn from a normally distributed population with mean μ = 30 and standard deviation σ = 2.3. [You may find it useful to reference the z table.]

a. Are the sampling distribution of the sample mean with n = 35 and n = 76 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 = 35 will have a normal distribution.

  • No, only the sample mean with n = 76 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 30.7 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.)


n Probability
35
76
Math   Statistics-And-Probability   
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Answer #1

(a) Ans : Yes, both the sample means will have a normal distribution.

(b)

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