Question

A local motel has 100 rooms. The occupancy rate for the winter months is 60%. Find the probability that in a given winter month fewer than 70 rooms will be rented. Use the normal distribution to approximate the binomial distribution.

Answer 1

Solution :

Given that,

p = 0.60

q = 1 - p =1 - 0.60=0.40

n = 100

Using binomial distribution,

Mean = = n * p = 100 *0.60=60

Standard deviation = = n * p * q = 100 *0.60*0.40=4.8990

Using continuity correction ,

P(x< 69.5 ) = P((x - ) / < (69.5 - 60) / 4.8990)

= P(z < 1.94)

Using z table

=0.9738

Probability = 0.9738