Mathematics 1670
Test 2 Chapters 5,6,7,8
Name: ______________________________
Student ID: ___________________
Instructor: Sarah Inkpen
Section:____________________
1. The shape of any uniform probability distribution is
A)
B)
C)
D)
Negatively skewed
Positively skewed
Rectangular
Bell shaped
2. Suppose that in a certain part of the world in any 50-year period the probability of a
major plague is 0.39, the probability of a major famine is 0.52 and the probability of
both a plague and a famine is 0.15. What is the probability of a famine given that
there is a plague.
A) 0.24
B) 0.288
C) 0.370
D) 0.385
3. A new drug has been developed that is found to relieve nasal congestion in 90 percent of
those with the condition. The new drug is administered to 300 patients with the condition.
What is the probability that more than 265 will be relieved of nasal congestion?
A) 0.0916
B) 0.1922
C) 0.8078
D) 0.3078
4. Each new employee is given an identification number. The personnel files are
arranged sequentially starting with employee number 0001. to sample the employees,
the number 0153 was first selected then numbers 0253, 0353, 0453 and so on became
members of this sample. This type of sampling is called:
A) Simple random sampling
B) Systematic sampling
C) Stratified random sampling
D) Cluster sampling
5. The mean amount spent by a family of four on food per month is $500 with a standard
deviation of $75. Assuming that the food costs are normally distributed, what is the
probability that a family spends less than $410 per month?
A) 0.2158
B) 0.8750
C) 0.0362
D) 0.1151
6. Which of the following is NOT true regarding the normal distribution?
A)
B)
C)
D)
Mean, median and mode are all equal
It has a single peak
It is symmetrical
The points of the curve meet the X-axis at z = –3 and z = 3
7. What is the area (percentage) under the normal curve between z = 0.0 and z = 2.0?
A)
B)
C)
D)
1.0000
0.7408
0.1359
0.4772
8. Companies proved to have violated pollution laws are being fined various amounts
with the following probabilities.
Fines (QR)
1000
10000
50000
100000
Probability
0.4
0.3
0.2
0.1
What are the mean and standard deviation for the fine variable? C
A)  x  40250,  x  39118
B)  x  40250,  x  45169
C)  x  23400,  x  31350
D)  x  23400,  x  85185
9. The mean score of a college entrance test is 500; the standard deviation is 75. The scores
are normally distributed. What percent of the students scored below 320?
A) About 50.82%
B) About 34.13%
C) About 7.86%
D) About 0.82%
10.
In a 1974 “Dear Abby” letter a woman lamented that she had just given birth to
her eighth child and all were girls! Her doctor assured her that the chance of the
eighth child being a girl was only 1 in 100. What was the real probability that
the eighth child would be a girl?
A) 0.5
B) 0.0039
C) 0.01
D) 0
11.
A large manufacturing firm tests job applicants who recently graduated from college.
The test scores are normally distributed with a mean of 500 and a standard deviation of
50. Management is considering placing a new hire in an upper level management
position if the person scores in the upper 6 percent of the distribution. What is the lowest
score a college graduate must earn to qualify for a responsible position?
A) 50
B) 625
C) 460
D) 578
12. Two normal distributions are compared. One has a mean of 10 and a standard deviation of
10. The second normal distribution has a mean of 10 and a standard deviation of 2.
Which of the following it true?
A) the locations of the distributions are different
B) the distributions are from two different families
C) the dispersions of the distributions are different
D) the dispersions of the distributions are the same
13.
Given the distribution of a discrete random variable X as shown
below, the expectation of X, E(X), is
A) 0.15
x
0
1
2
3
P (X = x)
0.15
0.20
0.35
0.30
B. 1.80
C. 0.90
D. 1.
14. A group of statistics students decided to conduct a survey at their university to find
the average (mean) amount of time students spend studying per week. Based on a simple
random sample, they surveyed 144 students. The statistics showed that students studied
an average of 20 hours per week with a standard deviation of 10 hours.
a) What is the standard error of the mean?
A)
B)
C)
D)
0.83
10
0.5
2
b) What is the probability that a sample mean would exceed 20 hours per week?
A)
1.0
B)
0.5
C)
1.96
D)
Cannot be calculated based on the given information.
c) What is the probability of finding a sample mean less than 18 hours?
A)
0.4820
B)
0.4920
C)
0.0080
D)
0.0180
d) What is the probability that average student study time is between 18 and 22
hours?
A)
0.9640
B)
0.0160
C)
0.0360
D)
0.9840
If n  7 and r  4 , what is n Pr ?
15.
a) 28
16.
b) 35
c) 840
d) 2401
A sales representative calls on four hospitals in Westchester County. It is immaterial
what order he calls on them. How many ways can he organize his calls?
A)
4
B)
24
C)
120
D)
37
17. There are 10 rolls of film in a box and 3 are defective. Two rolls are to be selected, one
after the other. What is the probability of selecting a defective roll followed by another
defective roll?
A) 1/2, or 0.50
B) 1/4, or 0.25
C) 1/120, or about 0.0083
D) 1/15, or about 0.07
18. The mean score on a college placement exam is 500 with a standard deviation of 100.
Ninety-five percent of the test takers score above what?
A)
260
B)
336
C)
405
D)
664
19. A soft-drink company produces a drink called Super-Drink. They advertise
355 ml on the can. The filling process follows a normal distribution with a
mean value of  = 357 ml with a standard deviation of  = 1.5 ml . What is the
probability that a randomly chosen drink is under-filled (that is has less than
the amount advertised on the can)?
a)
9.1 %
b)
9.5 %
c)
9.8 %
d)
10.6 %
20. The first card selected from a standard 52-card deck was a king. If it is returned to
the deck, what is the probability that a king will be drawn on the second selection?
A)
B)
C)
D)
1/4 or 0.25
1/13, or 0.077
12/13, or 0.923
1/3 or 0.33
21.The first card selected from a standard 52-card deck was a king. If it is NOT returned to
the deck, what is the probability that a king will be drawn on the second selection?
A) 1/3 or 0.33
B) 1/51, or 0.0196
C) 3/51, or 0.0588
D) 1/13 or 0.077
22.
The mean score of a college entrance test is 600; the standard deviation is 80.
The scores are normally distributed.
a) Label the normal curve
b) What score is the 70th percentile?
INVNORM (0.7,600,80)=642
c) What percent of the students fell between 600 and 800?
NORMALCDF(600,800,600,80)=0.494
[2]
[2]
[2]
23. David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does
not use a credit card. Past evidence indicates that 40% of all customers pay in cash.
During a one-hour period twenty-five customers buy gasoline at this station.
a)
What is the probability that at least ten pay in cash? [2]
P( X  10)  1  binomialcdf (25, 0.4,9)  0.575
b)
What is the probability that no more than twenty pay in cash? [2]
P( X  20)  Binomialcdf (25, 0.4, 20)  0.575
c)
What is the probability that more than ten and less than fifteen customers pay in
cash? [2]
P(10<x<15)=Binomialcdf(25,0.4,14)-Binomialcdf(25,0.4,10)=0.3798
24. A company is studying the number of monthly absences among its 125 employees. The
following probability distribution shows the likelihood that people were absent 0, 1, 2, 3,
4, or 5 days last month.
Number of days absent
0
1
2
3
4
5
Probability
0.60
0.20
0.12
0.04
0.04
0
Number of Days L1 and probability L2
a) What is the mean number of days absent? [2] 0.72
b) What is the standard deviation? [1] 1.08
c) Given the probability distribution, which of the following predictions is correct?
A) 60% of the employees will have more than one day absent for a month
B) There is a 0.04 probability that an employee will be absent 1 day during a month
C) There is a 0.12 probability that an employee will be absent 2 days during a
month
D) There is a 0.50 probability that an employee will be absent 0.72 days during a month.
25.
A large manufacturing firm tests job applicants who recently graduated from
college. The test scores are normally distributed with a mean of 500 and a
standard deviation of 50. Management is considering placing a new hire in an
upper level management position if the person scores in the upper 6 percent of the
distribution. What is the lowest score a college graduate must earn to qualify for
a responsible position? [3]
SAME AS NUMBER 11
26.
A survey found that the American family generates an average of 17.2 pounds of
glass garbage each year. Assume the standard deviation of the distribution is 2.5
pounds. Find the probability that the mean of the sample of 55 families will be
between 17 and 18 pounds. [3]
Normal distribution for a sample so must use sample error.
2.5
 0.337
55
Normalcdf(17,18,17.2,0.337)= 0.715
27. A grocery store manager notes that 35% of customers who buy a particular
product make use of a store coupon to receive a discount. Four people purchase
the product.
a) Identify the success probability, .
0.35
[1]
b) Develop a probability distribution showing probabilities
for the four customers using a coupon
X
0
1
2
3
4
P(X)
0.179
0.384
0.311
0.111
0.015
[3]
c) What is the probability that more than 2 customers used a coupon?
0.111+0.015=0.125
[2]
e) What is the expected number of customers using a coupon?
[2]
4 X 0.35 =1.4
f) What is the standard deviation for this problem?
[1]
4*0.35*0.65  0.96
28. A cage holds two litters of rats. One litter comprises 3 females and 4 males and
the other comprises of 2 females and 6 males. A random selection of 1 rat is
made. Complete the contingency table:
[4]
Males
Females
TOTAL
LITTER 1
4
3
7
LITTER 2
6
2
8
TOTAL
10
5
15
I.Find the probabilities that the rat is: (1 point each)
a) male
P(M)=10/15
b) female P(F)=5/15
c) Litter 1 (L1)=7/15
d) Litter 2 P(L2)=8/15
e) P(m Litter 1)
4/7
f) P (male or Litter 2) 10/15+ 8/15 – 6/15 = 12/15
29.
The coach of a track team can send only the top 5% of her runners to a
regional track meet. For the members of her team, times for a 1-km run are
normally distributed with a mean of 5.6 min and a standard deviation of 0.76
min. Be careful, the faster the runner the better!
a) Label the curve
[3]
b)
What is the cut-off time to determine which members of the team qualify for
the regional meet?
[2]
Invmorm(0.05,5.6,0.76)=4.35
c)
Her junior team consists of 20 runners what is the probability that the mean of
this time will be less than 5.5 minutes?
[2]
Sample Error
30.
0.76
 0.17 Normalcdf(0,5.5,5.6,0.17) = 0.278
20
Every day Morse attempts the crossword puzzle in his newspaper. The time taken,
X minutes, to complete the crossword may be modeled by a Normal Distribution
with mean 22 minutes and standard deviation 4.5 minutes.
a)
Calculate the probabilities that he takes
i)
less than 25 minutes to complete the crossword
[2]
Normalcdf(0,25,22,4.5)=0.7475
ii)
more that 15 minutes to complete the crossword.
[2]
1-Normalcdf(0,15,22,4.5)=0.94
iii)
between 15 and 25 minutes to complete the crossword.[2]
Normalcdf(16,24,22,4.5)=0.58
b)
What length of time would be enough for Morse to finish the
crossword on 95% of days?
Invnorm(0.95,22,4.5) = 29.4
[2]