if the probability is .65 that a person at a license plate renewal line in a sta

Question

if the probability is .65 that a person at a license plate renewal line in a state motor vehicle office will pay extra for a special commemorative license plate. Assume 15 randomly obseerved individuals are picked from this line

A) How do you call this probability distribution?

B) Is this probability distribution discrete or continuous?

C) Describe the shape of this probability distribution

D) What is the probability that exactly 5 will py extra for the special commemorativev license plate?

E) What is the probability more that 8 will pay extra for the special commemorative licsense plate?

F) Compute the expected value, variance and standard deviation of this probability distution.

Explanation / Answer

As each trial is independent and there are only two outcomes this is Binomial

X - no of persons at a license plate renewal line in a state motor vehicle office will pay extra for a special commemorative license plate is binomial with 15, 0.65

b) Discrete as no of persons can be only in natural numbers

c) Shape is bell symmetrical about mean.

d) P(X=5) = 15C5 (0.65)5(0.35)10

= 0.009612

e) P(X>8) =0.7548

f) E(X) = np = 9.78

Var(x) = npq = 3.4125

Std dev = 1.8473

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