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
[tex]z = \frac{x - \mu}{ \sigma} [/tex]
This means that:
[tex]P(135 \: < \: X \: < \: 175) = P( \frac{135 - 145}{16.5} \: < \: z \: < \frac{175 - 145}{ 16.5} )
[/tex]
We simplify to get:
[tex]P(135 \: < \: X \: < \: 175) = P( - 0.61\: < \: z \: < 1.82 )[/tex]
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:
[tex]P(135 \: < \: X \: < \: 175) =0.69[/tex]
The correct choice is C.
