A random sample is drawn from a population with mean = 59 and standard deviation

Question

A random sample is drawn from a population with mean = 59 and standard deviation = 4.9. Use Table 1.

a. Is the sampling distribution of the sample mean with n = 21 and n = 42 normally distributed?

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

b)No, both the sample means will not have a normal distribution.

c)No, only the sample mean with n = 21 will have a normal distribution.

d)No, only the sample mean with n = 42 will have a normal distribution.

b. Can you use the standard normal distribution to calculate the probability that the sample mean falls between 59 and 61 for both sample sizes?

a)Yes, for both the sample sizes, standard normal distribution could be used.

b)No, for both the sample sizes, standard normal distribution could not be used.

c)No, only for the sample size with n = 21, standard normal distribution could be used.

d)No, only for the sample size with n = 42, standard normal distribution could be used.

c. Calculate the probability that the sample mean falls between 59 and 61 for n = 42. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Explanation / Answer

Answer to the quesiton is as follows:

a.

d. is right. Sample size has to more than 30 for the distribution
to be normal

b.

d)No, only for the sample size with n = 42, standard normal distribution could be used. For n=21 we have to use students-t distribution

c. P(59<X<61)
= P(59-59/(4.9) <t<61-59/(4.9)
= P(0<t<.41)
= .6591-.5000
= .1591
(all rounding offs done according to question)

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