Question

In a parking garage, the probability that a randomly-selected numbered parking spot has an illegally parked car is .05. supposed that whether a car is parked illegally or not has no bearing on the legality of other cars. The number of illegally parked cars will be counted based on a random sample of 60 parking spots. of course each time that a sample os size 60 is taken a number of illegally parked cars could change. what is the standard deviation of the number of illegally parked cars when selecting random samples of 60 spots?

a. 1.69

b.2.85

c.3.00

d.8.89

*the answer is a, I just don't know how to get to that as an answer.

Answer 1

Sample size , n = 60

P[ an illegally parked car ] = p = 0.05

q = 1 - p = 1 - 005 = 0.95

Var = n*p*q (Binomial )

Var = 60*0.05*0.95

Var = 2.85

standard deviation = sqrt(var)

standard deviation = sqrt(2.85)

standard deviation = 1.69