Question

A local rental car agency has 200 cars. The rental rate for the winter months is 60%. Find the probability that in a given winter month fewer than 140 cars will be rented. Use the normal distribution to approximate the binomial distribution.

Answer 1

`P(Z\leq2.89)=0.9981`

Explanation:

Sample size
`n=200`

Rental Rate
`R=60\%`

Probability =(P<140)

Generally the equation for mean of distribution is mathematically given by

`\mu=nR\\\\\mu=200*0.60\\\\\mu=120`

Generally the equation for Standard deviation of distribution is mathematically given by

`\sigma=√(npq)`

`\sigma=√(200*0.60*0.40)`

`\sigma=6.9`

Therefore

Z-score for x=140 is

`Z=(x-\mu)/(\sigma)`

`Z=(140-120)/(6.9)`

`Z=2.89`

From table

`P(Z\leq2.89)=0.9981`