Question

1. Salaries for entry level employees working in a certain industry are normally distributed with a mean of $37,098 and a standard deviation of $1,810.

What proportion workers in this industry have entry level salaries greater than $40,000?

**Round your answer to 4 decimal places.**

**2.**Salaries for entry level employees working in
a certain industry are normally distributed with a mean of $38,211
and a standard deviation of $1,531.

What proportion workers in this industry have entry level salaries between $36,000 and $40,000?

**Round your answer to 4 decimal places.**

**3.**Salaries for entry level employees working in
a certain industry are normally distributed with a mean of $37,056
and a standard deviation of $1,903.

Find the percentile P_{84} for entry level salaries of
employees working in this industry.

**Round your answer to 2 decimal places.**

Answer #1

1)

for normal distribution z score =(X-μ)/σ | |

here mean= μ= | 37098 |

std deviation =σ= | 1810.000 |

proportion workers in this industry have entry level salaries greater than $40,000:

probability
=P(X<40000)=(Z<(40000-37098)/1810)=P(Z<1.6)=0.9456 |

(please try 0.9452 if this comes wrong due to rounding error)

2)

probability
=P(36000<X<40000)=P((36000-38211)/1531)<Z<(40000-38211)/1531)=P(-1.44<Z<1.17)=0.879-0.0749=0.8044 |

(please try 0.8041 if this comes wrong due to rounding error)

3)

for 84th percentile critical value of z= | 0.99 | ||

therefore corresponding value=mean+z*std deviation= |
38948.45 |

8) Salaries for entry level employees working in a certain
industry are normally distributed with a mean of $37,419 and a
standard deviation of $1,897.
What proportion workers in this industry have entry level
salaries greater than $40,000?
Round your answer to 4 decimal places.

26) Salaries for entry level employees working in a certain
industry are normally distributed with a mean of $37,152 and a
standard deviation of $1,739.
What proportion workers in this industry have entry level
salaries less than $40,000?
Round your answer to 4 decimal places.
Please explain each step in detail. Thank
you!

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