A bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 200 and a standard deviation of 50. if an applicant is randomly selected, find the probability of a rating that is between 200 and 275. your answer should be a decimal rounded to the fourth decimal place.

the probability of a rating that is between 200 and 275 is 0.4332

Step-by-step explanation:

Given the data in the question;

if an applicant is randomly selected, the probability of a rating that is between 200 and 275

mean μ = 200

standard deviation σ = 50

P( 200 < X < 275 ) = P( X-μ / σ  < x-μ / σ <  X-μ / σ )

P( 200 < X < 275 ) = P( 200-200 / 50  < x-μ / σ <  275-200 / 50 )

= P( 0/50 < Z <  75/50 )

= P( 0.00 < Z < 1.50 )

P(Z < 1.50) - P(Z < 0.0)

from the standard normal table

P(Z < 1.50) = 0.9332

P(Z < 0.0) = 0.5000

so

P( 200 < X < 275 ) = 0.9332 - 0.5000

P( 200 < X < 275 ) = 0.4332

Therefore, the probability of a rating that is between 200 and 275 is 0.4332

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

answer: -8.2562234e+13