A bank's loan officer rates applicants for credit.The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50.If an applicant is randomly selected,what percentage can be expected to be between 200 and 275?

A) 6.68%
B) 43.32%
C) 93.32%
D) 42.37%
E) 5.00%

Question

Cailyn Jordan · Accepted Answer

Final Answer : B, Explanation :  Since the ratings follow a normal distribution with mean 200 and standard deviation 50, we can standardize the scores using the formula z = (x - μ)/σ. Then, to find the percentage of applicants between 200 and 275, we compute:z1 = (200 - 200)/50 = 0z2 = (275 - 200)/50 = 1.5Using a standard normal distribution table or calculator, we can find the proportion of values between z1 and z2, which is approximately 0.4332 or 43.32%. Therefore, the answer is B.

A bank's loan officer rates applicants for credit.The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50.If an applicant is randomly selected,what percentage can be expected to be between 200 and 275?

A) 6.68%
B) 43.32%
C) 93.32%
D) 42.37%
E) 5.00%

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A bank's loan officer rates applicants for credit.The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50.If an applicant is randomly selected,what percentage can be expected to be between 200 and 275?A) 6.68%B) 43.32%C) 93.32%D) 42.37%E) 5.00%

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Learning Objectives

Learning Objectives

Related questions

A bank's loan officer rates applicants for credit.The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50.If an applicant is randomly selected,what percentage can be expected to be between 200 and 275?

A) 6.68%
B) 43.32%
C) 93.32%
D) 42.37%
E) 5.00%