A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 240.0 and a standard deviation of 48.0. If an applicant is randomly selected, find the probability of a rating that is between 164.0 and 216.0.
A)
21.18648%
B)
25.18648%
C)
17.18648%
D)
29.18648%
E)
33.18648%
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probability of a rating that is between 164.0 and 216.0. = 25.18648%
Step-by-step explanation:
Mean = 240
SD = 48
Z score = (Value - mean)/SD
Z score of 164
= ( 164 - 240)/48
= -1.583
=> 5.68 %
Z score of 164
= ( 216 - 240)/48
= -0.5
=> 30.85 %
% between 164.0 and 216.0. = 30.85 - 5.68 %
= 25.17 %
from given option 25.18648% is closest
probability of a rating that is between 164.0 and 216.0. = 25.18648%
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