Question

) A bank's loan officer randomly selects an applicant's credit rating. The credit ratings are normally distributed with a mean of 110 and a standard deviation of 25. a) Find the probability that the applicant's credit rating is less than 135.

b) Find the probability that the applicant's credit rating is greater than 100.

c) Find the probability that the applicant's credit rating is between 60 and 160.

Answer 1

Solution :

Given that,

mean = = 110

standard deviation = = 15

a ) P( x < 135 )

P ( x - / ) < ( 135 - 110 / 25)

P ( z < 25 / 25 )

P ( z < 1 )

= 0.8413

Probability = 0.8413

b ) P (x > 100 )

= 1 - P (x < 100 )

= 1 - P ( x -  / ) < ( 100- 110 / 25)

= 1 - P ( z <- 10 / 25 )

= 1 - P ( z < -0.4 )

Using z table

= 1 - 0.3446

= 0.6554

Probability = 0.6554

c ) P ( 60 < x < 160)

P ( 60 - 110 / 25) < ( x -  / ) < ( 160 - 110 / 25)

P ( - 50 / 25 < z < 50 / 25 )

P (- 2< z < 2 )

P ( z < 2 ) - P ( z < - 2 )

Using z table

= 0.9772 - 0.0228

= 0.9544

Probability = 0.9544