A random sample is drawn from a normally distributed population with mean mu = 1

Question

A random sample is drawn from a normally distributed population with mean mu = 19 and standard deviation sigma = 1.8. Use Table 1. a. Are the sampling distributions of the sample mean with n = 27 and n = 54 normally distributed? Yes No b. Can you use the standard normal distribution to calculate the probability that the sample mean is less than 19.9 for both sample sizes? Yes No c. Calculate the above probabilities for both sample sizes. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

Explanation / Answer

c) for n=27; std error =std deviaiton/(n)1/2 =0.3464

hence P(X<19.9)=P(Z<(19.9-19)/0.3464)=P(Z<2.5981)=0.9953

for n=54 ; std error =0.2449

hence P(X<19.9)=P(Z<3.6742)=0.9999

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