A lightbulb manufacturer wants to estimate the number of defective bulbs contained in a typical box shipped by the company. Production personnel at this company have recorded the number of defective bulbs found in each of the 1000 boxes shipped during the past week. These data are provided in P8_11.XLS. 

a. Generate an appropriate histogram for the given distribution of 1000 numbers of defective bulbs. Characterize this distribution. Also, compute the mean and standard deviation of the given numbers.

b. Repeatedly choose simple random samples of size 3 from the original distribution given in P8_11.XLS. Record the sample mean for each of 500 sampling repetitions and generate an appropriate histogram of the resulting sampling distribution. Characterize this sampling distribution and compute its mean and standard deviation.

c. Repeatedly choose simple random samples of size 6 from the original distribution given in P8_11.XLS. Record the sample mean for each of 500 sampling repetitions and generate an appropriate histogram of the resulting sampling distribution. Characterize this sampling distribution and compute its mean and standard deviation.

d. Repeatedly choose simple random samples of size 12 from the original distribution given in P8_11.XLS. Record the sample mean for each of 500 sampling repetitions and generate an appropriate histogram of the resulting sampling distribution. Characterize this sampling distribution and compute its mean and standard deviation.

e. Explain the changes in your constructed sampling distributions as the sample size was increased from n = 3 to n = 12. In particular, how does the sampling distribution you constructed in part d compare to the original distribution (where n = 1) you described in part a?