Consider a normal random variable with mean 50 and
standard deviation 10, and a random sample of size 80 from which we are
to compute the values of , the sample mean. What is the probability
of getting a value of as low as 46?BITMAPSETAnswer0.2214in0.205in0ina1
2.
Suppose a working widget deteriorates very little with
age. That is, a widget that has been running for some time will have nearly
the same failure probability during the following hour as it had during its
first hour of operation. Then, the failure times have an exponential
distribution
P(T≤t) of the form
1 - e-. Given that
the widget has a mean life of 5 years, what is the probability that the
widget will have a lifetime exceeding 7.5 years? If the widget is guaranteed
for 2 years, what percentage of such widgets can be expected to need
replacement while under warranty?BITMAPSETAnswer0.2214in0.205in0ina2
3.
A widget has a mean life of 5 years with a standard
deviation of 2 years. Assuming a normal distribution, what is the
probability that the widget will have a lifetime exceeding 7.5 years? If the
widget is guaranteed for 2 years, what percentage of such widgets can be
expected to need replacement while under warranty?BITMAPSETAnswer0.2214in0.205in0ina3
4.
The mean of a continuous distribution with probability
density function f (u) is the integral
uf (u)du = μ of the product of the variable and the probability density
function. The variance is the integral
u - μf (u)du. Find the mean and variance for each of the
continuous distributions discussed in this chapter.BITMAPSETAnswer0.2214in0.205in0ina4
5.
The mean of a discrete distribution with probability
density function f (u) is the sum
uf (u) = μ,
and the variance is
u - μf (u) = σ2.
Find the mean and variance for the discrete distributions discussed
in this chapter.
If the probability density function for a distribution is
f (n) = , what is the mean of the distribution?
What is the variance?BITMAPSETAnswer0.2214in0.205in0ina5
6.
A die is cast until a 4 appears. What is the
probability that it must be cast more than five times?
BITMAPSETAnswer0.2214in0.205in0ina6
7.
A telephone switchboard handles 600 calls on average
during a single rush hour. The board can make a maximum of 20 connections
per minute. Use the Poisson distribution to evaluate the probability that
the board will be overtaxed during any given minute of a rush hour.
BITMAPSETAnswer0.2214in0.205in0ina7
8.
Find the probability that
x2≤4 for a normal
distribution with mean 1 and standard deviation 1.