Question

A binomial probability distribution has p = .20 and n = 100.

If required, round your answers to four decimal places.
a. What are the mean and standard deviation?

=__________
=___________
b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution?
SelectYesNoItem 3

Explain.

SelectYes, because np?5 and n(1-p)?5 No, because np?5 and n(1-p)?5 Yes, because np?5 or n(1-p)?5 No, because np?5 or n(1-p)?5 Item 4
c. What is the probability of exactly 23 successes?
d. What is the probability of 16 to 24 successes?
e. What is the probability of 16 or fewer successes?

Answer 1

Mean = 0.2(100) = 20

Variance = 0.2×0.8×100 = 16

Standard deviation = 4

Yes, np > 5 & nq > 5

Answer 2

Mean = 0.2(100) = 20

Variance = 0.2×0.8×100 = 16

Standard deviation = 4

Yes, np > 5 & nq > 5