A banker finds that the number of times people use automated-teller machines in a year are normally distributed with a mean of 40.0 and a standard deviation of 11.4. What is the percentage of customers who use them less than 25 times?

Answer 1

9.34%.

Given that the distribution is said to be normal, we can use a z-score table to obtain the desired percentage after standardizing the values we gave to a z-score value.

First, note that we have #mu = 40.0# and #sigma = 11.4#. This describes a normal distribution of #N(40.0,11.4^2)#. We can use the formula for the z-score to convert the value of 25 times into its representative z-score:
#z = (x-mu)/sigma = (25 - 40.0)/11.4 = (-15)/11.4 = -1.32#

We simply use a z-score table to find the z-score we just determined (-1.32) and use the table to find the left-tail area under the normal curve in order to determine the percentage of customers who use the ATMs fewer than 25 times.

This translates to an area of 0.0934, or approximately 9.34% of all customers, according to a single table.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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