Just focusing on the \"Full Time Overall Undergraduate Salaries\" and assuming a

Question

Just focusing on the "Full Time Overall Undergraduate Salaries" and assuming a normal distribution of salaries, answer the following questions: What is the probability a graduate of this school earning between $55,000 and $75,000? We would like to know how much the top 5% earn. Based on the information you are given, estimate the cut-off value to make it into the top 5% in terms of yearly salaries. A random person tells you they earn $34, 563 per year. Would you expect this person to have graduated from this school?

Explanation / Answer

Solution:

We are given that the full time overall undergraduate salaries are normally distributed.

We are given mean = 64354 and SD = 12833

Part a

Here, we have to find P(55000<X<75000)

P(55000<X<75000) = P(X<75000) – P(X<55000)

Now, we have to find P(X<75000)

The z-score formula is given as below:

Z = (X – mean) / SD

Z = (75000 – 64354) / 12833

Z = 0.82958

P(X<75000) = P(Z<0.82958) = 0.796612

Now, we have to find P(X<55000)

Z = (55000 – 64354) / 12833

Z = -0.7289

P(X<55000) = P(Z<-0.7289) = 0.233031

P(55000<X<75000) = P(X<75000) – P(X<55000)

P(55000<X<75000) = 0.796612 – 0.233031

P(55000<X<75000) = 0.56358

Required Probability = 0.56358

Part b

The z-score for top 5% or below 95% is given as 1.644854

The formula for X is given as below:

X = mean + Z*SD

X = 64354 + 1.644854*12833

X = 85462.4

Cut-off Salary = $85462.4

Part c

First we have to find P(X34563)

Z = (X – mean) / SD

Z = (34563 - 64354) / 12833

Z = -2.3214

P(X34563) = P(Z< -2.3214) = 0.010132

This probability is less than 5% or 0.05, so we would not expect that this person to have graduated from this school.

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