Question

3. Auditors at a small community bank randomly sample 100 withdrawal transactions made during the
week atan ATM machine located near the bank's main branch. Over the past 2 years, the average
withdrawal amount has been $50 with a standard deviation of $40. Since audit investigations are
typically expensive, the auditors decide to not initiate further investigations if the mean transaction
amount of the sample is between $45 and $55. What is the probability that in any given week, there
will be an investigation?
A. 1.25%
B. 2.5%
C. 10.55%
E 50%
distribution, or distribution of sample​

Answer 1

Answer:

We're in the xbar distribution (sample mean distribution, or distribution of sample means). In this case the center is at mu = 50 and the standard error is SE = s/sqrt(n) = 40/sqrt(100) = 40/10 = 4

This distribution is normally distributed because of the central limit theorem. The fact that n = 100 makes n > 30 true indicates that we can use this idea.

Using a calculator, the value of P(45 < x < 55) is roughly 0.7887

Subtracting 1 from that value gives 1-0.7887 = 0.2113 which converts to 21.13%

That rounds to 21.1% so you have the correct answer. Nice work.

You can use an online tool such as this one to check your work.

That specific calculator also provides the sketch of the shaded area.

Hope it helps you

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