1. A survey of the students in a psychology class revealed that there were 19 females
and 8 males. Ot the 19 females, only 4 had no brothers or sisters, and 3 of the
males were also the only child in the household. If a student is randomly selected
from t
1. b. 20/27
c. 4/27
2. Aj ar contains 10 red marbles and 30 blue marbles.
a. If you randomly select 1 marble from the jar, what is the probability of obtaining a red marble?
b. If you take a random sample of n = 3 marbles from the jar and the first two
marbles are both blue,
2. a. p = f = 0.25
b- P = 45 = 0.25. Remember that random sampling requires sampling with replacement.
3. Suppose that you are going to select a random sample of /; = 1 score from the
distribution in Figure 6.2. Find the following probabilities:
a. p(X > 2)
b. p(X > 5)
c. p(X < 3)
3. a. p=7/10
b- P = 0.1
c- P = m = 0.3
1. Find the proportion of a normal distribution that corresponds to each of the following sections:
a. z < 0.25
b. z > 0.80
c. z < -1.50
d. z > -0.75
1. a. p ~ 0.5987
b. p = 0.2119
c. p = 0.0668
d. p = 0.7734
2. For a normal distribution, find the z-score location that divides the distribution as
follows:
a. Separate the top 20% from the rest.
b. Separate the top 60% from the rest.
c. Separate the middle 70% from the rest
2. a. c = 0.84
b. z = -0 .2 5
c. z = � 1.04 and + 1.04
3. The tail will be on the right-hand side of a normal distribution for any positive
z-score. (True or false)
True
1. For a normal distribution with a mean of |a = 60 and a standard deviation of
ct = 12, find each probability value requested.
a. p(X > 66)
b. p(X < 75)
c. p(X < 57)
d. p (48 < X < 72)
1. a. p = 0.3085
b. p = 0.8944
c. p = 0.4013
d. p = 0.6826
2. Scores on the Mathematics section of the SAT Reasoning Test form a normal
distribution with a mean of |i = 500 and a standard deviation of ct = 100.
a. If the state college only accepts students who score in the top 60% on this test,
what is the minimu
2. a. z = -0.25; X = 475
b. z = 1.28; X = 628
c. z = �0.67; X =433 and X =567
3. What is the probability of selecting a score greater than 45 from a positively
skewed distribution with p = 40 and ct = 10? (Be careful.)
3. You cannot obtain the answer. The unit normal table cannot be used to answer this question
because the distribution is not normal.
. Under what circumstances is the normal distribution an accurate approximation of
the binomial distribution?
1. When pn and qn are both greater than 10
2. In the game Rock-Paper-Scissors, the probability that both players will select the
same response and tie is p = y, and the probability that they will pick different
responses is p = �. If two people play 72 rounds of the game and choose their
responses
2. With� p = j and1 q = y, the binomial distribution is normal with p = 24 and a = 4;2
p(X > 28.5) = p(z >1.13) = 0.1292.
3. If you toss a balanced coin 36 times, you would expect, on the average, to get
18 heads and 18 tails. What is the probability of obtaining exactly 18 heads in
36 tosses?
3. X = 18 is an interval with real limits of 17.5 and 18.5. The real limits correspond to z = �0.17,
and a probability ofp = 0.1350.
1. A local hardware store has a "Savings Wheel" at
the checkout. Customers get to spin the wheel and,
when the wheel stops, a pointer indicates how much
they will save. The wheel can stop in any one of
50 sections. Of the sections, 10 produce 0% off,
20 s
1. a. p = 1/50 = 0.02
b. p = 10/50 = 0.20
c. p = 20/50 = 0.40
2. A psychology class consists of 14 males and 36 females.
If the professor selects names from the class list using
random sampling,
a. What is the probability that the first student
selected will be a female?
b. If a random sample of n = 3 students is se
2. a. p = 36/50 = 0.72
b. p = 14/50 = 0.28 (Remember, a random sample requires replacement.)
3. W hat are the two requirem ents that must be satisfied
for a random sample?
3. The two requirements for a random sample are: (1) each individual has an equal chance of being selected, and (2) if more than one individual is selected, the probabilities must stay constant for all selections.
4. What is sampling with replacement, and why is it used?
3. The two requirements for a random sample are: (1) each individual has an equal chance of being selected, and (2) if more than one individual is selected, the probabilities must stay constant for all selections.
5. Draw a vertical line through a normal distribution for
each of the following z-score locations. Determine
whether the tail is on the right or left side of the line
and find the proportion in the tail.
a. z = 2.00
b. z = 0.60
c. z = -1.30
d. z = -0.30
5. a. tail to the right, p = 0.0228
b. tail to the right, p = 0.2743
c. tail to the left, p = 0.0968
d. tail to the left, p = 0.3821
6. Draw a vertical line through a normal distribution for
each of the following z-score locations. Determine whether the body is on the right or left side of the line
and find the proportion in the body.
a. z = 2.20
b. z = 1.60
c. z = -1.50
d. z = -0.70
6. a. body to the left, p = 0.9861
b. body to the left, p = 0.9452
c. body to the right, p = 0.9332
d. body to the right, p = 0.7580
7. Find each of the following probabilities for a normal
distribution.
a. p(z > 0.25)
b. p(z > -0.75)
c. p(z < 1.20)
d. p(z < � 1.20)
7. a. p(z > 0.25) = 0.4013 c. p(z < 1.20) = 0.8849
b. p(z > -0.75) = 0.7734 d. p(z < -1.20) = 0.1151
8. What proportion of a normal distribution is located
between each of the following z-score boundaries?
a. z = -0.50 and z = +0.50
b. z = -0.90 and z = +0.90
c. z = - 1.50 and z
8. a. p = 0.3830
b. p = 0.6318
c. p = 0.8664
9. Find each of the following probabilities for a normal
distribution.
a. pi-0.25 < z < 0.25)
b. p(-2.00 < z < 2.00)
c. p (-0.30 < z < 1.00)
d . p ( - 1.25 < z < 0.25)
9. a. p = 0.1974 c. p = 0.4592
b. p = 0.9544 d. p = 0.4931
10. Find the z-score location of a vertical line that
separates a normal distribution as described in
each of the following.
a. 20% in the tail on the left
b. 40% in the tail on the right
c. 75% in the body on the left
d . 99% in the body on the right
10. a. z = -0.84 c. z = 0.67
b. z = 0.25 d. z = -2.33
11. Find the z-score boundaries that separate a normal
distribution as described in each of the following.
a. The middle 20% from the 80% in the tails.
b. The middle 50% from the 50% in the tails.
c. The middle 95% from the 5% in the tails.
d. The middle
11. a. z = �0.25 c. z = �1.96
b. z = �0.67 d. z = �2.58
12. For a normal distribution with a mean of p = 80 and
a standard deviation of ct = 20, find the proportion of
the population corresponding to each of the following
scores.
a. Scores greater than 85.
b. Scores less than 100.
c. Scores between 70 and 90.
12. a. p(z > 0.25) = 0.4013
b. p(z < 1.00) = 0.8413
c. p(-0.50 < z < 0.50) = 0.3830
13. A normal distribution has a mean of p = 50 and
a standard deviation of ct = 12. For each of the
following scores, indicate whether the tail is to the
right or left of the score and find the proportion of
the distribution located in the tail.
a. X = 53
13. a. tail to the right, p = 0.4013
b. tail to the left, p = 0.3085
c. tail to the right, p = 0.0668
d. tail to the left, p = 0.1587
14. IQ test scores are standardized to produce a normal
distribution with a mean of p = 100 and a standard
deviation of cr = 15. Find the proportion of the
population in each of the following IQ categories.
a. Genius or near genius: IQ greater than 140
b.
14. a. z = 2.67, p = 0.0038
b. p(1.33 < z < 2.67) = 0.0880
c. p(-0.67 < z < 0.60) = 0.4743
15. The distribution of scores on the SAT is approximately
normal with a mean of p = 500 and a standard
deviation of cr = 100. For the population of students
who have taken the SAT,
a. What proportion have SAT scores greater than 700?
b. What proportion h
15. a. z = 2.00, p = 0.0228
b. z = 0.50, p = 0.3085
c. z = 1.28, X = 628
d. z = -0.25, X = 475
16. The distribution of SAT scores is normal with |i = 500
and ct = 100.
a. What SAT score, X value, separates the top 15% of
the distribution from the rest?
b. W hat SAT score, X value, separates the top 10% of
the distribution from the rest?
c. What SAT
16. a. z = 1.04, X = 604
b. z = 1.28, X = 628
c. z = 2.05, X = 705
17. A recent newspaper article reported the results
of a survey of well-educated suburban parents.
The responses to one question indicated that by
age 2, children were watching an average of
|i = 60 minutes of television each day. Assuming
that the distri
17. a. p(z > 1.50) = 0.0668
b. p(z < -2.00) = 0.0228
18. Information from the Department of Motor Vehicles
indicates that the average age of licensed drivers is
p = 45.7 years with a standard deviation of cr = 12.5
years. Assuming that the distribution of drivers' ages
is approximately normal,
a. What propo
18. a. z = 0.34, p = 0.3669
b. z = -1.26, p = 0.1038
19. A consumer survey indicates that the average
household spends p = $185 on groceries each
week. The distribution of spending amounts is
approximately normal with a standard deviation
of cr = $25. Based on this distribution,
a. What proportion of the po
19. a. z = 0.60, p = 0.2743
b. z = -1.40, p = 0.0808
c. z = 0.84, X = $206 or more
20. Over the past 10 years, the local school district has
measured physical fitness for all high school freshmen.
During that time, the average score on a treadmill
endurance task has been p = 19.8 minutes with a
standard deviation of cr = 7.2 minutes. As
20. a. p(z > 0.72) = 0.2358
b. p(z > 1.42) = 0.0778
c. p(z < -1.36) = 0.0869
21. Rochester, New York, averages p = 21.9 inches of
snow for the month of December. The distribution
of snowfall amounts is approximately normal with
a standard deviation of ct = 6.5 inches. This year, a
local jewelry store is advertising a refund of 50%
21. p(X > 36) = p(z > 2.17) = 0.0150 or 1.50%
22. A multiple-choice test has 48 questions, each with four
response choices. If a student is simply guessing at the
answers,
a. What is the probability of guessing correctly for
any question?
b. On average, how many questions would a student
get correct
22. a. p = �
b. ? = 12
c. ? = ?9 = 3 and for X = 15.5, z = 1.17, and p = 0.1210
d. For X = 14.5, z = 0.83, and p = 0.2033
23. A true/false test has 40 questions. If a students is
simply guessing at the answers,
a. What is the probability of guessing correctly for
any one question?
b. On average, how many questions would the student
get correct for the entire test?
c. What is
23. a. p = �
b. ? = 20
c. ? = ?10 = 3.16 and for X = 25.5, z = 1.74, and p = 0.0409
d. For X = 24.5, z = 1.42, and p = 0.0778
24. A roulette wheel has alternating red and black
numbered slots into one of which the ball finally
stops to determine the winner. If a gambler always
bets on black to win, what is the probability of
winning at least 24 times in a series of 36 spins?
(No
24. p = q = 1/2, and with n = 36 the normal approximation has ? = 18 and ? = 3. Using the lower real limit of 23.5, p(X > 23.5) = p(z > 1.83) = 0.0336.
25. One test for ESP involves using Zener cards. Each
card shows one of five different symbols (square,
circle, star, cross, wavy lines), and the person being
tested has to predict the shape on each card before it
is selected. Find each of the probabiliti
25. a. With five options, p = 1/5 for each trial. ? = 20 and ? = 4 For X = 20, z = �0.13
and p = 0.1034.
b. For X = 30.5, z = 2.63 and p = 0.0043.
c. ? = 40 and ? = 5.66 For X = 49.5, z = 1.68 and p = 0.0465
26. A trick coin has been weighted so that heads occurs
with a probability ofp = j , and /j(tails) = j . If you
toss this coin 72 times,
a. How many heads would you expect to get on
average?
b. What is the probability of getting more than 50
heads?
c. Wha
26. a. = pn = 48
b. z = 0.63, p = 0.2643
c. p(0.38 < z < 0.63) = 0.0877
27. For a balanced coin:
a. What is the probability of getting more than
30 heads in 50 tosses?
b. What is the probability of getting more than
60 heads in 100 tosses?
c. Parts a and b both asked for the probability of
getting more than 60% heads in a ser
27. a. With n = 50 and p = q = 1/2, you may use the normal approximation with ? = 25 and ? = 3.54. Using the upper real limit of 30.5, p(X > 30.5) = p(z > 1.55) = 0.0606.
b. The normal approximation has ? = 50 and ? = 5. Using the upper real limit of 60.5
28. A national health organization predicts that 20% of
American adults will get the flu this season. If a
sample of 100 adults is selected from the population,
a. What is the probability that at least 25 of the people
will be diagnosed with the flu? (Be
28. a. ? = 20 and ? = 4 For X = 24.5, z = 1.13, and p = 0.1292.
b. For X = 14.5, z = -1.38, and p = 0.0838.