Question

A local rental car agency has 50 cars. The rental rate for the winter months is 60%. Find the probability that in a given winter month at least 35 cars will be rented. Use the normal distribution to approximate the binomial distribution. Round the standard deviation to three decimal places to work the problem.

Answer 1

Solution :

Given that,

p = 0.60

q = 1 - p =1-0.60=0.40

n = 50

Using binomial distribution,

= n * p = 50*0.60=30

= n * p * q = 50*0.60*0.40=3.464

Using continuity correction

,P(x >35 ) = 1 - P(x <34.5 )

= 1 - P((x - ) / < (34.5-30) / 3.464)

= 1 - P(z <1.30 )   

Using z table   

= 1-0.9032

probability= 0.0968