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.

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this: for the value of 215

And we can find this probability using the complement rule and with the normal standard distribution or excel we got:

Step-by-step explanation:

Let X the random variable that represent the ratings of applicants from a population, and for this case we know the distribution for X is given by:

Where and

We select a sample size of n =40. We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this: for the value of 215

And we can find this probability using the complement rule and with the normal standard distribution or excel we got:

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step-by-step explanation:

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