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 ?

Answer 1

Answer:

E) 0.977

Explanation:

From the question we have that the mean number of transactions is 478 and standard deviation is 64.

$\implies \mu=478$ and $\sigma=478$

We want to find the proportion of daily transaction that is greater than 350 i.e $P(X\:>\:350)$

We  first find the z-score using the formula:

$Z=\frac{x-\mu}{\sigma}$

$Z=\frac{350-478}{64}=-2$

Reading from the standard normal distribution table $P(X\:<\:350)=0.0228$

Note that:

$P(X\:>\:350)=1-P(X\:<\:350)$

$\implies P(X\:>\:350)=1-0.0228=0.9772$

Therefore the proportion of daily transactions greater than 350 is 0.977

The last option is correct