Please complete the following in EXCEL. Show excel formulas for full credit. Ass

Question

Please complete the following in EXCEL. Show excel formulas for full credit.

Assuming a normal distribution, compute the following probabilities, use Excel functions and standard mathematical notation.

a) Probability that a single person drawn at random has a salary less than $90,000

b) Probability that a single person drawn at random has a salary greater than $100,000

c) Probability that a single person drawn at random has a salary between $80,000 and $110,000

d) Probability that 36 peopole drawn at random have a mean salary less than $90,000

Ohio Salary 61500 68800 69200 75700 76000 77500 77600 78700 78700 78700 81300 83800 83800 84200 84300 84600 84600 87700 87700 89400 90700 90700 94700 95400 97200 97600 101300 101800 103400 103400

Explanation / Answer

a)P(X<90000) =norm,dist(90000,85666.67,10668.04,true)=0.6577

b)P(X>100000)=1-P(X<100000)=1-norm.dist(100000,85666.67,10668.04,true)=1-0.9105=0.0895

c)P(80000<X<110000)=norm.dist(110000,85666.67,10668.04,true)-norm.dist(80000,85666.67,10668.04,true)

=6911

d)for 36 people' std error =std deviation/(n)1/2 =1778.01

hence P(X<90000)=norm,dist(90000,85666.67,1778.01,true)=0.9926

Ohio Salary 61500 68800 69200 75700 76000 77500 77600 78700 78700 78700 81300 83800 83800 84200 84300 84600 84600 87700 87700 89400 90700 90700 94700 95400 97200 97600 101300 101800 103400 103400 mean 85666.67 std deviation 10668.04

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