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 t…

Question

asked May 20, 2020 72.3k views

1 Answer

Tsunamis · Answer 1 · 2020-05-24T21:46:48+0000

Answer:

E) 0.977

Step-by-step 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:

$Z=(x-\mu)/(\sigma)$

Z=(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