# Question: In which of the following binomial distributions does the normal

In which of the following binomial distributions does the normal distribution provide a reasonable approximation? Use computer commands to generate a graph of the distribution and compare the results to the “rule of thumb.” State your conclusions.

a. n = 10, p = 0.3

b. n = 100, p = 0.005

c. n = 500, p = 0.1

d. n = 50, p = 0.2

MINITAB

Insert the specific n and p as needed in the procedure below. Use the Make Patterned Data commands in Exercise 6.71, replacing the first value with 0, the last value with n, and the steps with 1.

Use the Binomial Probability Distribution commands on page 251, using C2 as optional storage.

Use the Scatterplot Simple commands for the data in C1 and C2. Select Data View, Data Display, Project Lines to complete the graph.

Excel

Insert the specific n and p as needed in the procedure below. Use the RANDOM NUMBER GENERATION Patterned Distribution commands in Exercise 6.71, replacing the first value with 0, the last value with n, the steps with 1, and the output range with A1. Activate cell B1; then use the Binomial Probability Distribution commands on pages 251-252.

Use the Insert > commands for the data in columns A and B Choosing the Select Data subcommand remove Series 1.

a. n = 10, p = 0.3

b. n = 100, p = 0.005

c. n = 500, p = 0.1

d. n = 50, p = 0.2

MINITAB

Insert the specific n and p as needed in the procedure below. Use the Make Patterned Data commands in Exercise 6.71, replacing the first value with 0, the last value with n, and the steps with 1.

Use the Binomial Probability Distribution commands on page 251, using C2 as optional storage.

Use the Scatterplot Simple commands for the data in C1 and C2. Select Data View, Data Display, Project Lines to complete the graph.

Excel

Insert the specific n and p as needed in the procedure below. Use the RANDOM NUMBER GENERATION Patterned Distribution commands in Exercise 6.71, replacing the first value with 0, the last value with n, the steps with 1, and the output range with A1. Activate cell B1; then use the Binomial Probability Distribution commands on pages 251-252.

Use the Insert > commands for the data in columns A and B Choosing the Select Data subcommand remove Series 1.

**View Solution:**## Answer to relevant Questions

In order to see what happens when the normal approximation is improperly used, consider the binomial distribution with n = 15 and p = 0.05. Since np = 0.75, the rule of thumb (np > 5 and nq > 5) is not satisfied. Using the ...Referring to Example 6.21 (p. 302): a. Calculate P(x < 3|B(25, 3 )). b. How good was the normal approximation? Explain. a. Using a computer or a random number table, simulate the drawing of 250 samples, each of size 18, from the uniform probability distribution of single-digit integers, 0 to 9. b. Find the mean for each sample. c. Construct ...A certain population has a mean of 500 and a standard deviation of 30. Many samples of size 36 are randomly selected and the means calculated. a. What value would you expect to find for the mean of all these sample means? ...In Example7. 5, explain how the 0.9773 and the 0.0228 were obtained and what they are used for.Post your question