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Answer:
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.
<em>Let X = ratings for credit</em>
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.