Question

# 1. Salaries for entry level employees working in a certain industry are normally distributed with a...

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?

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?

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 P84 for entry level salaries of employees working in this industry.

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

(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

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