The Binomial Distribution Worksheet (Page 4 of 6) in pdf

The Binomial Distribution Worksheet Page 4

Example (Ex. 4.13, p. 206) Suppose a poll of 20 employees is taken in a large company. The

purpose is to determine x, the number who favor unionization. Suppose that 60% of all the

company's employees favor unionization (p = .6, q = .4, n = 20)

a. Find the mean and standard deviation of x.

µ = 20×0.6 = 12, σ

= 20×0.6×0.4 = 4.8, σ = √4.8 = 2.19

b. Use Table I in Appendix D to find the probability that x ≤ 10. Repeat using TI-83

P(x ≤ 10) = 0.245

Tables:

P(x ≤ k) = P(at most k successes) = binomcdf(n,p,k)

TI-83:

2nd→DISTR→A:binomcdf(….. →ENTER

binomcdf(20,.6,10) = .2446628

c. Use Table I to find the probability that x > 12. Repeat using TI-83

P(x > 12) = 1 - P(x ≤ 12) = 1 - .584 = .416

Tables:

TI-83:

1 - binomcdf(20,.6,12) = .415893

d. Find the probability that x ≥ 8.

P(x ≥ 8) = 1 - P(x ≤ 7) = 1 - binomcdf(20,.6,7) = .97897

e. Use Table I to find the probability that x = 11. Repeat using TI-83. Also compute it using binomial

formula.

P(x = 11) = P(x ≤ 11) - P(x ≤ 10) = .404 - .245 = .159

Tables:

TI-83:

P(x = k) = P(exactly k successes) = binompdf(n,p,k)

2nd→DISTR→0:binompdf(……. →ENTER

P(x = 11) = binompdf(20,.6,11) = .159738

The Binomial Distribution Worksheet Page 4