Question

A mail order company has a 9% success rate. If it mails advertisement to 500 people, find the probability of getting fewer than 38 sales.

Answer 1

EXPLANATION

Let's consider the facts:

Success rate= 9% = 0.09 (in decimal form)

Number of advertised people = 500

So, n=500, p=0.09 and 1-p=0.91

By definition, we know that:

Mean = np = 500*0.09 = 45

Now, we need to find the standard deviation:

$SD=\sigma=\sqrt[]{np(1-p)}=\sqrt[]{500\cdot0.09\cdot0.91}=\sqrt[]{40.95}=6.399218\equiv6.4$

So the Probability of getting fewer than 38 sales is given by the following relationship:

P(X<38):

$Z=\frac{38-45}{6.399}=\frac{-7}{6.399}=-1.0939$

Look up z= -1.0939 on a z-table.

The obtained value is z= 0.13786 or %13.786

This means that there is a %13.78 of fewer than 38 sales.