Question

The average rent of a one bed room apartment in Johnson city is $600 with a standard deviation of $100. Assume that rent is normally distributed find the following: (6 marks) a. What is the probability that rent for the apartment will be between $400 and $800? (-1.75), (-1.40) b. What is the probability that the rent will between $300 and $900? C. What is the probability that the rent will be less than $700?

Answer 1

Let X be the rent of one bed rooms in Johnson City. Given, X~N(600, 100²).

a) The probability that rent for the apartment will be between $400 and $800 is=

P(400<X<800)

=P[(400-600) /100<(X-600) /100<(800-600) /100]

=P(-2<Z<2) [where Z=(X-600) /100~N(0, 1) ]

=P(Z<2) -P(Z<-2)

=0.9772-0.0228(from the standard normal table)

=0.9544

Thus, the required probability is 0.9544

b) the probability that the rent will be between $300 and $900 is=

P(300<X<900)

=P[(300-600) /100<Z<(900-600) /100]

=P(-3<Z<3)

=P(Z<3) -P(Z<-3)

=0.9987-0.0013(from the standard normal table)

=0.9974

Thus, the required probability is 0.9974.

c) The probability that the rent will be less than $700 is=

P(X<700)

=P[Z<(700-600) /100]

=P(Z<1)

=0.3413(from the standard normal table)

Thus the required probability is 0.3413.