Discuss the below:
Q1. Suppose that the random variable x is normally distributed with mean = 1,000 and standard deviation = 100. Sketch and find each of the following probabilities:
a. P(1,000<_x<_1,200) e. P(x<_700)
b. P(x>1,257) f. P(812<_x<_913)
c. P(x<1,035) g. P(x>891)
d. P(857<_x<_1,183) h. P(1,050<_x<_1,250)
Q2. An investment broker reports that the yearly returns on common stocks are approximately normally distributed with a mean return of 12.4 percent and a standard deviation of 20.6 percent. On the other hand, the firm reports that the yearly returns on tax-free municipal bonds are approximately normally distributed with a mean return of 5.2 percent and a standard deviation of 8.6 percent. Find the probability that a randomly selected
a. Common stock will give a positive yearly return.
b. Tax-free municipal bond will give a positive yearly return.
c. Common stock will give more than a 10 percent return.
d. Tax-free municipal bond will give more than a 10 percent return.
e. Common stock will give a loss of at least 10 percent.
f. Tax-free municipal bond will give a loss of at least 10 percent.
Q3. Suppose that yearly health care expenses for a family of four are normally distributed with a mean expense equal to $3,000 and a standard deviation of $500. An insurance company has decided to offer a health insurance premium reduction if a policyholder's health care expenses do not exceed a specified dollar amount. What dollar amount should be established if the insurance company wants families having the lowest 33 percent of yearly health care expenses to be eligible for the premium reduction?