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 40 different applicants are randomly selected, find the probability that their mean is above 215. Round your answer to four decimal places. A. 0.4713 B. 0.3821 C. 0.0287 D. 0.1179

Probability that their mean is above 215 is 0.0287.

Step-by-step explanation:

We are given that 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.

For this, 40 different applicants are randomly selected.

Let X = ratings for credit

So, X ~ N()

Now, the z score probability distribution for sample mean is given by;

         Z = ~ N(0,1)

where, = population mean = 200

            = standard deviation = 50

            = sample mean

           n = sample of applicants = 40

So, probability that their mean is above 215 is given by = P( > 215)

    P( > 215) = P( > ) = P(Z > 1.897) = 1 - P(Z 1.897)

                                                         = 1 - 0.97108 = 0.0287

Therefore, probability that their mean is above 215 is 0.0287.

step-by-step explanation:

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