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A bank's loan officer rates applicants fro credit. The ratings are normally distributed with a mean...

A bank's loan officer rates applicants fro credit. The ratings are normally distributed with a mean of 620 and a standard deviation of 50. If 40 applicants are randomly selected, find the probability that their mean credit score is between 575 and 630. Round to 4-decimal places.

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Expert Solution

Solution :

Given that ,

mean =   = 620

standard deviation = = 50

n = 40

= 620

=  / n= 50/ 40=7.9057

P(575<     <630 ) = P[(575-620) / 7.9057 < ( - ) /   < (630-620) / 7.9057 )]

= P( -5.69< Z <1.26 )

= P(Z <1.26 ) - P(Z < -5.69)

Using z table

=0.8962-0

=0.8962

probability=  0.8962

orchestra answered 2 years ago
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