Question

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

If the daily earnings follow a normal distribution, what is the probability that the plumber earns between $135 and $175 on a given day?

A) 0.54
B) 0.63
C) 0.69
D) 0.77

Answer 1

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 = (x - \mu)/( \sigma)`

This means that:

`P(135 \: < \: X \: < \: 175) = P( (135 - 145)/(16.5) \: < \: z \: < (175 - 145)/( 16.5) )</p><p>`

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.