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 P₈₄ 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