Question

The distribution of the number of transactions performed at a bank each day is approximately normal with mean 478 transactions and standard deviation 64 transactions. Which of the following is closest to the proportion of daily transactions greater than 350?

a. 0.023
b. 0.046
c. 0.954
d. 0.477
e. 0.977

Answer 1

e. 0.977

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 478, \sigma = 64`

Which of the following is closest to the proportion of daily transactions greater than 350?

This is 1 subtracted by the pvalue of Z when X = 350. So

`Z = (X - \mu)/(\sigma)`

`Z = (350 - 478)/(64)`

`Z = -2`

`Z = -2` has a pvalue of 0.023

1 - 0.023 = 0.977

So the correct answer is:

e. 0.977