3. The recent average starting salary for new college graduates in computer info

Question

3. The recent average starting salary for new college graduates in computer information systems is $47,500. Assume salaries are normally distributed with a standard deviation of $4,500.

PLEASE SHOW WORK AND FORMULAS USED. EXCEL, ETC

a. What is the probability of a new graduate receiving a salary between $45,000 and $50,000?

b. What is the probability of a new graduate getting a starting salary in excess of $50,000?

c. What percent of starting salaries are no more than $42,250?

d. What is the cutoff for the bottom 5% of the salaries?

e. What is the cutoff for the top 3% of salaries?

Explanation / Answer

Answer:

We are given

Mean = µ = 47500

Population SD = = 4500

Salaries follow normal distribution.

Z score formula is given as below:

Z = (X - µ)/

a. What is the probability of a new graduate receiving a salary between $45,000 and $50,000?

Solution:

We have to find P(45000<X<50000)

P(45000<X<50000) = P(X<50000) – P(X<45000)

For X<50000

Z = (50000 – 47500)/4500 = 0.555556

P(X<50000) = P(Z< 0.555556) = 0.710743

For X<45000

Z = (45000 – 47500)/4500 = -0.55556

P(X<45000) = P(Z< -0.55556) = 0.289257

P(45000<X<50000) = P(X<50000) – P(X<45000)

P(45000<X<50000) = 0.710743 - 0.289257 = 0.421485

Required probability = 0.421485

b. What is the probability of a new graduate getting a starting salary in excess of $50,000?

Solution:

We have to find P(X>50000)

P(X>50000) = 1 – P(X<50000)

For X<50000

Z = (50000 – 47500)/4500 = 0.555556

P(X<50000) = P(Z< 0.555556) = 0.710743

P(X>50000) = 1 – P(X<50000)

P(X>50000) = 1 – 0.710743

P(X>50000) = 0.289257

Required probability = 0.289257

c. What percent of starting salaries are no more than $42,250?

Solution:

We have to find P(X<42250)

Z = (42250 – 47500)/4500 = -1.16667

P(X<42250) = P(Z< -1.16667) = 0.121673

Required probability = 0.121673

d. What is the cutoff for the bottom 5% of the salaries?

Solution:

X = µ + Z*

Z for bottom 5% = -1.64485

X = µ + Z*

X = 47500 + (-1.64485)*4500

X = 47500 – 1.64485*4500 = 40098.18

Required cutoff salary = $40098.16

e. What is the cutoff for the top 3% of salaries?

Solution:

X = µ + Z*

Z for top 3% = 1.880794

X = 47500 + 1.880794*4500 = 55963.57

Required cutoff salary = $55963.57

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