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

Answers ( )

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    2022-01-12T17:45:02+00:00

    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.

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45:7+7-4:2-5:5*4+35:2 =? ( )