1.
What is the total area under the
normal curve?
2.
A study was conducted that resulted in
the following relative frequency histogram. Determine whether or not the
histogram indicates that a normal distribution could be used as a model for the
variable.
3.
Find the area of the indicated region
under the standard normal curve.
The area between z = 0 and z = 1.2 under
the standard normal curve is.
4.
Find the area of the indicated region
under the standard normal curve.
The area between z = 0 and z = 1.2 under
the standard normal curve is.
5.
Assume the random variable x is normally distributed with mean μ = 88 and standard deviation
σ = 5. Find the indicated
probability.
6.
Assume a member is selected at random
from the population represented by the graph. Find the probability that the
member selected at random is from the shaded area of the graph. Assume the
variable x is normally distributed.
7.
Assume a member is selected at random
from the population represented by the graph. Find the probability that the
member selected at random is from the shaded area of the graph. Assume the
variable x is normally distributed.
8.
The mean incubation time for a type of
fertilized egg kept at 100.6oF is 23 days. Suppose that the
incubation times are approximately normally distributed with a standard
deviation of 1 day.
a.
What is the probability that a
randomly selected fertilized egg hatches in less than 22 days?
b.
What is the probability that a
randomly selected fertilized egg hatches between 21 to 23 days?
c.
What is the probability that a
randomly selected fertilized egg takes over 24 days to hatch?
9.
The life span of a battery is normally
distributed, with a mean of 2500 hours and a standard deviation of 50 hours.
What percent of batteries have a life span that is more than 2575 hours? Would
it be unusual for a battery to have a life span that is more than 2575 hours?
Explain yours reasoning.
10.
Use the standard normal table to find the z-score that corresponds to the
cumulative area 0.7517. If the area is not in the table, use the entry closest
to the area. If the area is halfway between two entries, use the z-score halfway between the
corresponding z-scores.
11.
Find the indicated z-score shown in the graph to the right.
12.
Find the indicated z-score shown in the graph.
13.
Find the z-scores for which 97% of the distribution’s area lies between –z and z.
14.
The time spent(in days) waiting for a
heart transplant in two states for a patients with type A+ blood can
be approximated by a normal distribution, as shown in the graph to the right.
Complete parts (a) and (b) below.
a.
What is the shortest time spent
waiting for a heart that would still place in the top 15% of waiting times?
b.
What is the longest time spent waiting
for a heart that would still place in the bottom 15% of waiting times?
15.
A population has a mean μ = 90 and a standard deviation σ = 27. Find the mean and standard
deviation of a sampling distribution of sample means with sample means with
sample size n=81
16.
Determine whether the statement is
true or false. If it is false, rewrite it as a true statement.
As the size of a sample increases, the
mean of the distribution of sample means increases.
17.
The population mean and standard
deviation are given below. Find the required probability and determine whether
the given sample mean would be considered unusual.
For a sample of n = 75, find the probability of a sample mean being greater than
213 if μ = 212 and
σ = 6.1.
18.
Use the central limit theorem to find
the mean and standard error of the means of the indicated sampling
distribution. Then sketch a graph of the sampling distribution.
The per capita consumption of red meat
by people in a country in a recent year was normally distributed, with a mean
of 115 pounds and a standard deviation of 37.2 pounds. Random samples of size
20 are drawn from this population and the mean of each sample is determined.
19.
A machine used to fill gallon-sized
paint cans is regulated so that the amount of paint dispensed has a mean of 124
ounces and a standard deviation of 0.40 ounce. You randomly select 50 cans and
carefully measure the contents. The sample mean of the cans is 123.9 ounces.
Does the machine need to be reset? Explain your reasoning.
20.
The sample size n, probability of success p,
and probability of failure q are
given for a binomial experiment. Decide whether you can use the normal
distribution to approximate the random variable x.
n = 17 p = 0.32 q
= 0.68
21.
Use the correction for continuity and
determine the normal probability statement that corresponds to the binomial
probability statement.
Binomial Probability P(x < 113)
22.
Decide whether you can use the normal
distribution to approximate the binomial distribution. If you can, use the
normal distribution to approximate the indicated probabilities and sketch their
graph. If you cannot, explain why and use the binomial distribution to find the
indicated probabilities.
Five percent of workers in a city use
public transportation to get to work. You randomly select 273 workers and ask
them if they use public transportation to get to work. Complete parts (a)
through (d).
a.
Find the probability that exactly 19
workers will say yes.
b.
Find the probability that at least 9
workers will say yes.
c.
Find the probability that fewer than
19 workers will say yes.
d.
A transit authority offers discount
rates to companies that have at least 30 employees who use public
transportation to get to work. There are 549 employees in a company. What is
the probability that the company will not get the discount?
Can the normal distribution be used to
approximate the binomial distribution?
23.
A drug tester claims that a drug cures
a rare skin disease 81% of the time. The claim is checked by testing the drug
on 100 patients. If at least 74 patients are cured, the claim will be accepted.
Find the probability that the claim
will be rejected assuming that the manufacturer’s claim is true. Use the normal
distribution to approximate the binomial distribution if possible.
