A random sample is drawn from a population with mean = 73 and standard deviation

Question

A random sample is drawn from a population with mean = 73 and standard deviation : 6.1 Use Table a. Is the sampling distribution of the sample mean with n = 18 and n = 46 normally distributed? O Yes, both the sample means will have a normal distribution No, both the sample means will not have a normal distribution. O No, only the sample mean with n = 18 will have a normal distribution. No, only the sample mean with n - 46 will have a normal distribution between 73 and 76 for both sample sizes? O Yes, for both the sample sizes, standard normal distribution could be used. b. Can you use the standard normal distribution to calculate the probability that the sample mean falls No, for both the sample sizes, standard normal distribution could not be used O No, only for the sample size with n 18, standard normal distribution could be used No, only for the sample size with n 46, standard normal distribution could be used. C. Calculate the probability that the sample mean falls between 73 and 76 for n = 46, (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability

Explanation / Answer

a) no only the sample with n=46 wiull have a normal distirbution.

b)

no only for the sample size with n=46.................

c)

std errror =std deviation/(n)1/2 =6.1/(46)1/2 =0.8994

hence probability=P(73<X<76)=P(0.5<Z<3.34)=0.9996-0.5 =0.4996

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