Question

The average starting salary of this year’s graduates of a large university (LU) is $60,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. 1. What is the probability that a randomly selected LU graduate will have a starting salary of at least $66,000? 2. Individuals with starting salaries of less than $45,000 receive a free class. What percentage of the graduates will receive a free class? 3. According to the textbook, what percentage of values fall one standard deviation from the mean? Two standard deviations from the mean? 4. What are the minimum and the maximum starting salaries of the middle 95.4% of the LU graduates?

Answer 1

Solution:-

Avg. Salary( μ)=$60,000

Std. Deviation(σ)=$5,000

1.)

P(X<=$66,000)=P(((X-μ)/σ)<=((66,000-60,000)/5000))

=P(Z<=1.2)

=0.8849 ...ans

2.)

P( starting salaries of less than $45,000 )=P(X<45000)

P(X<45000)=P(((X-μ)/σ)<((45000-60,000)/5000))

=P(Z<=-3)

=0.0014 ..ans

3.)

As per the empirical rule:-

Within One Std. Deviation of mean total 68% values fall.

Within Two Std. Deviation of mean total 95% values fall.

4.)