## 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 norma

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

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5 days 2022-01-12T17:43:14+00:00 1 Answer 0 views 0

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

This means that:

We simplify to get:

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:

The correct choice is C.