A random sample is drawn from a population with mean = 55 and standard deviation

Question

A random sample is drawn from a population with mean = 55 and standard deviation = 4.6. Use Table 1. a. Is the sampling distribution of the sample mean with n = 13 and n = 37 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 = 37 will have a normal distribution. b. Can you use the standard normal distribution to calculate the probability that the sample mean falls between 55 and 57 for both sample sizes? Yes, for both the sample sizes, standard normal distribution could be used. No, for both the sample sizes, standard normal distribution could not be used. No, only for the sample size with n = 13, standard normal distribution could be used. No, only for the sample size with n = 37, standard normal distribution could be used. c. Calculate the probability that the sample mean falls between 55 and 57 for n = 37. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Explanation / Answer

a) No, only the sample mean with n = 37 will have a normal distribution.

b)  No, only for the sample size with n = 37, standard normal distribution could be used

c)

probability that the sample mean falls between 55 and 57 :

for normal distribution z score =(X-)/ here mean=       = 55.000 std deviation   == 4.6 sample size       =n= 37 std error=x=/n= 0.7562

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