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.

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nuhulawal20 nuhulawal20 · Answer 1 · 2021-02-25T01:52:01+01:00

Answer:

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