Consider a binomial experiment with n=20 and p=0.90. Answer these questions with

Question

Consider a binomial experiment with n=20 and p=0.90. Answer these questions without using the binomial tables.

a. Compute P(X=19)

b. Compute P(X18)

c. Compute P(X17)

d. Compute E(X)

e. Compute Var(X) and .  

2) A survey of all employees at a large corporation reported that 25% of these employees feel that their company is loyal to them. Suppose 10 employees are selected randomly and will be interviewed about company loyalty. Do not use the binomial tables for these questions.

a. Explain how the selection of 10 employees is a binomial experiment.

b. What is the probability that none of the 10 employees will say that their company is loyal to them?

c. What is the probability that no more than 2 employees say that their company is loyal to them?

d. What is the probability that at least 9 employees say that their company is not loyal to them?

3) Suppose X is a binomial random variable with n=100 and p=.80. Use the binomial tables to answer the following questions.

a. P(X=75)

b. P(X14)

c. P(X<62)

Explanation / Answer

a) P(x=19) = 20C19 (0.9)19(0.1)

= 0.2702

b) P(X>=18) = P(X=19,18,20)

= 0.6769

c) P(X<=17) = 0.3231

d) E(x) = np = 18

e) Var(x) = npq = 1.8

sigma = 1.342

-------------------------------

a) Each employee is independent of selection and there are two outcomes hence binomial

b) P(X=0) = 0.0563

c) P(x<=2) = 0.5256

d) P(X>=9) = 2.956x10-5

-------------------------

a) P(X=75)=0.0439

b) P(X>=14) = 0.9999

c) P(X<62) = 1.529x10-5

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