Question

A plumber's daily earnings have a mean of $145 per day with a standard deviation of $16.50.

Answer 1

Step-by-step explanation:

The plumber's daily earnings have a mean of $145 per day with a standard deviation of

$16.50.

We want to find the probability that the plumber earns between $135 and

$175 on a given day, if the daily earnings follow a normal distribution.

That is we want to find P(135 <X<175).

Let us convert to z-scores using

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

This means that:

$P(135 \: < \: X \: < \: 175) = P( \frac{135 - 145}{16.5} \: < \: z \: < \frac{175 - 145}{ 16.5} )$

We simplify to get:

$P(135 \: < \: X \: < \: 175) = P( - 0.61\: < \: z \: < 1.82 )$

From the standard n normal distribution table,

P(z<1.82)=0.9656

P(z<-0.61)=0.2709

To find the area between the two z-scores, we subtract to obtain:

P(-0.61<z<1.82)=0.9656-0.2709=0.6947

This means that:

$P(135 \: < \: X \: < \: 175) =0.69$

The correct choice is C.