Download Homework 1 2.1 The random variable X has a

Homework 1
2.1 The random variable X has a normal distribution with mean 60 and standard
deviation 12.
(a) The probability is 0.10 that this random variable takes a value less than what
number?
(b) Find the number K such that the probability is 0.90 that the random variable takes
a value between 60-K and 60+K.
(c) The random variable Y is defined by Y=200-2X. Find the mean and standard
deviation of Y.
2.2 A particular brand of tie has a lifetime whose distribution is normal with mean
40,000 miles and standard deviation 10,000 miles.
(a) The probability is 0.95 that one of these tires has a lifetime of more than how
many miles?
(b) Four of these tires are chosen at random. The probability is 0.95 that their average
lifetime is more than how many miles?
2.3 A mutual fund has a very large portfolio of stocks. A random sample of nine of
these showed the following percentage returns over a year. [See text for data].
Assume that the population distribution is normal.
The annual percentage returns of nine stocks from a portfolio:
8.2 15.7 3.1 4.7 12.8 9.6 18.3 11.4 10.2
(a) Find the sample mean.
(b) Find the sample variance.
(c) Find the sample standard deviation.
(d) Find a 99% confidence interval for the population mean.
(e) Find a 95% confidence interval for the population variance.
(f) Find a 90% confidence interval for the population standard deviation.
2.4 Carefully explain why a 95% confidence interval for a population parameter will be
wider than a 90% confidence interval for that parameter based on the same
information.