Question

The average starting salary of this year’s graduates of a large university (LU) is $55,000 with a standard deviation of $4,000. 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 $52,700?
2. Individuals with starting salaries of less than $45,00 receive a free class. What percentage of the graduates will receive the free class?
3. What percent of graduates will have their salaries one standard deviation from the mean?
4. What is the range of salaries that are one standard deviation from the mean?

Answer 1

µ = 55000

sd = 4000

a) $P(X>52700)=P(\frac{X-\mu}{\sigma}>\frac{52700-\mu}{\sigma})$

                                     $=P(Z>\frac{52700-55000}{4000})$

                                     = P(Z > -0.575)

                                     = 1 - P(Z < -0.575)

                                     = 1 - 0.28265

                                     = 0.71735

b) $P(X<45000)=P(\frac{X-\mu}{\sigma}<\frac{45000-\mu}{\sigma})$

                                    $=P(Z<\frac{45000-55000}{4000})$

                                    = P(Z < -2.5)

                                    = 0.0062

                                    = 0.62%

c) P(within one standard deviations from the mean) = P(-1 < Z < 1) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 = 68.26%

d) Lower value = µ - sd = 55000 - 4000 = 51000

Upper value = µ + sd = 55000 + 4000 = 59000