Questions: 1-9
Q1.
The ages of a group of 50 women are approximately normally
distributed with a mean of 47 years and a standard deviation of 6 years. One
woman is randomly selected from the group, and her age is observed.
a. Find the probability that her age will fall
between 53 and 62 years.
b. Find the probability that her age will fall
between 46 and 54 years.
c. Find the probability that her age will be
less than 32 years.
d. Find the probability that her age will
exceed 42 years.
Q2.
Almost all companies utilize some type of year-end
performance review for their employees. Human Resources(HR) at the university
of Texas health Science Center provides guidelines for supervisors rating their
subordinates. For example raters are advised to examine their ratings for a
tendency to be too lenient or too harsh. According to HR, “if you have this
tendency, consider using a normal distribution-10% of employees (rated)
exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable.”
Suppose you are rating an employee’s performance on a scale of 1(lowest) to
100(highest). Also assume the ratings follow normal distribution with a mean of
50 and a standard deviation of 12. Complete parts a and b.
a) What is the lowest rating you should give to
an “exemplary” employee if you follow the University’s HR guidelines?
b) What is the lowest rating you should give to
an “competent” employee if you follow the University’s HR guidelines?
Q3.
Financial analysts who make forecasts of stock prices are categorized as either "buy-side" analysts or "sell-side" analysts. Mean and standard deviation of the forecast errors for both types of analysts are shown in the table. Assume the distribution of forecast errors are approximately normally distributed.
Buy-Side Analysts |
Sell-Side Analysts | |
Mean |
0.87 |
-0.06 |
Standard Deviation |
1.96 |
0.82 |
a. Find the probability that a
buy-side analyst has a forecast error of +2.02 or higher.
b. Find the probability that a sell-side analyst has a forecast error of +2.02 or higher.
Q4. Q5. Q6.
Q7. Q8. Q9.