Find the mean of the given probability distribution.
1)
A police department reports that the
probabilities that 0, 1, 2, and 3 burglaries will
be reported in a given day are 0.50, 0.40, 0.09,
and 0.01 respectively.
2)
The random variable X is the number of
siblings of a student selected at random from a
particular secondary school. Its probability
distribution is given in the table.
x 0 1 2 3 4 5
P(X = x) 7
24 13
48 3
16 7
48 1
16 1
24
Provide an appropriate response.
3)
Computer chips often contain surface
imperfections. For a certain type of computer
chip, 9% contain no imperfections, 22% contain
1 imperfection, 26% contain 2 imperfections,
20% contain 3 imperfections, 12% contain 4
imperfections, and the remaining 11% contain
5 imperfections. Let X represent the number of
imperfections in a randomly chosen chip.
a. Specify the probability distribution for the
number of imperfections in a randomly chosen
chip.
b. Find the expected number of imperfections
in a randomly chosen chip
Find the indicated probability for the normally distributed
variable.
4)
The lengths of human pregnancies are
normally distributed with a mean of 268 days
and a standard deviation of 15 days. What is
the probability that a pregnancy lasts at least
300 days?
5)
The weekly salaries of teachers in one state are
normally distributed with a mean of $490 and
a standard deviation of $45. What is the
probability that a randomly selected teacher
earns more than $525 a week?
6)
A bank's loan officer rates applicants for credit.
The ratings are normally distributed with a
mean of 200 and a standard deviation of 50. If
an applicant is randomly selected, find the
probability of a rating that is between 200 and
275.
7)
A bank's loan officer rates applicants for credit.
The ratings are normally distributed with a
mean of 200 and a standard deviation of 50. If
an applicant is randomly selected, find the
probability of a rating that is between 170 and
220.
8)
The incomes of trainees at a local mill are
normally distributed with a mean of $1,100
and a standard deviation $150. What
percentage of trainees earn less than $900 a
month?
9)
Assume that the weights of quarters are
normally distributed with a mean of 5.67 g and
a standard deviation 0.070 g. A vending
machine will only accept coins weighing
between 5.48 g and 5.82 g. What percentage of
legal quarters will be rejected?
10)
The diameters of bolts produced by a certain
machine are normally distributed with a mean
of 0.30 inches and a standard deviation of 0.01
inches. What percentage of bolts will have a
diameter greater than 0.32 inches?
Use the empirical rule to solve the problem.
11)
The lifetimes of lightbulbs of a particular type
are normally distributed with a mean of 360
hours and a standard deviation of 8 hours.
What percentage of the bulbs have lifetimes
that lie within 2 standard deviations of the
mean?
12)
The systolic blood pressure of 18
-
year
-
old
women is normally distributed with a mean of
120 mmHg and a standard deviation of 12
mmHg. What percentage of 18-year-old
women have a systolic blood pressure that lies
within 3 standard deviations of the mean?
13)
At one college, GPA's are normally distributed
with a mean of 2.6 and a standard deviation of
0.4. What percentage of students at the college
have a GPA between 2.2 and 3?
Use a table of areas for the standard normal curve to find
the required z-score.
14)
Find the z
-
score for which the area under the
standard normal curve to its left is 0.04
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