a. Find P(4  x  6) for a random sample of size 4 drawn from a normal population with   5 and   2.

b. Use a computer to randomly generate 100 samples, each of size 4, from a normal probability distribution with   5 and   2. Calculate the mean, x, for each sample.

c. How many of the sample means in part b have values between 4 and 6? What percentage is that?

d. Compare the answers to parts a and

c, and explain any differences that occurred.
MINITAB (Release 14)

a. Input the numbers 4 and 6 into C1. Use the CUMULATIVE NORMAL PROBABILITY DISTRIBUTION commands on page 329, replacing the mean with 5, the standard deviation with 1 (2/4), the input column with C1, and the optional storage with C2. Find CDF(6)  CDF(4).

b. Use the Normal RANDOM DATA commands on page 327, replacing generate with 100, store in with C3–C6, mean with 5, and standard deviation with 2. Use the ROW STATISTICS commands on page 368, replacing input variables with C3–C6 and store result in with C7.

c. Use the HISTOGRAM commands on page 61 for the data in C7. Select Labels, Data Labels, Label Type; use y-value levels. To adjust the histogram, select Binning with midpoint and midpoint positions 0:10/1.
Excel

a. Input the numbers 4 and 6 into column A. Activate cell B1. Use the CUMULATIVE NORMAL DISTRIBUTION commands on page 329, replacing X with A1:A2. Find CDF(6)CDF(4).

b. Use the Normal RANDOM NUMBER GENERATION commands on page 328, replacing number of variables with 4, number of random numbers with 100, mean with 5, standard deviation with 2, and output range with C1. Activate cell G1. Use the AVERAGE INSERT FUNCTION commands in Exercise 7.13b on page 368, replacing Number1 with C1:F1.

c. Use the RANDOM NUMBER GENERATION Patterned Distribution commands in Exercise 6.66 on page 336, replacing the first value with 0, the last value with 9, the steps with 1, and the output range with H1. Use the HISTOGRAM commands on page 61 with column G as the input range, column H as the bin range, and column I as the output range.

TI-83/84 Plus

a. Use the CUMULATIVE NORMAL PROBABILITY commands on page 330, replacing the Enter with 4,6,5,1). (The standard deviation is 1;

from 2/4.)

b. Use the Normal RANDOM DATA and STO commands on page 328, replacing the Enter with 5,2,100). Repeat these commands three more times, storing data in L2, L3, and L4, respectively.

Choose: STAT  EDIT  1:Edit Highlight: L5 (column heading)

Enter: (L1L2L3L4)/4

c. Use the HISTOGRAM and TRACE commands on page 62 to count. Enter 0,9,1,0,45,1 for the Window.