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

Answer:

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

Step-by-step 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

$\sigma=\sqrt{npq}$

$\sigma=\sqrt{200*0.60*0.40}$

$\sigma=6.9$

Therefore

Z-score for x=140 is

$Z=\frac{x-\mu}{\sigma}$

$Z=\frac{140-120}{6.9}$

$Z=2.89$

From table

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