PRACTICE TEST 2 REVIEW (pink)
Math 153 Name: ________________________________
3/23/05 Test 2A
44444SHOW ALL WORK IF POSSIBLE FOR PARTIAL CREDIT!
(6 points)
2) The New York statelotto game consnsists of choosing 6 numbers from the numbers 1, 2, …, 59.
a) Find the number of ways of choosing 6 numbers from a set of 59 numbers.
b) What is the probability of winning the game if two sets of 6 numbers are selected? Select the best answer. Approximately,
a) 0.1017 b) 2.2 x 10-8 c) 2.2 x 108 d) 4.4 x 10-8 e) 4.4 x 108
(9 points)
3) Associated Press ran the following headline on February 6, 2002: “Study: Sun Lamps Double Cancer Risk.” Suppose that a survey of 1000 people is conducted, and the following information is obtained.
|
|
Skin Cancer |
No Skin Cancer |
|
|
Used tanning devices |
20 |
80 |
100 |
|
Did NOT use tanning devices |
90 |
810 |
900 |
|
|
|
|
1000 |
a) Find the probability of getting skin cancer if tanning devices were used. _____________
b) Find the probability of getting skin cancer if tanning devices were NOT used. ____________
c) Find the relative risk of getting skin cancer comparing people who used tanning devices to people who did NOT use tanning devices.
___________
(6 points)
4) A tax company prepares tax returns for businesse and reports that 12% of its businesses are audited. Out of four businesses selected at random, what is the probability at exactly two are audited? Show all work and round off to four decimal places.
________________________
(10 points)
5) In March,2002, the Supreme Court agreed to hear a case involving a high school’s policy of drug testing all students who participate in extracuricular activities. Suppose a screening test is developed to test for heroin use. Suppose that the probability that a randomly chosen student tests positive for heroin is 2%. The screening test is developed so that a positive test result should mean the person has used the drug. Assume that the following conditional probabilities are known.
P(Test + | the person used heroin) = .95
P(Test - | the person has NOT used heroin) = .96
a) Assume that 10,000 people are tested. Complete the table below.
|
|
Test + |
Test - |
|
|
Has used heroin |
|
10 |
200 |
|
Has NOT used heroin |
|
9408 |
|
|
|
|
|
10,000 |
a) Complete the table above (5 numbers).
Find the following conditional probabilities. Round off to 4 decimal places.
a) P(person has used heroin | Test +) = ___________________________
b) P(person has NOT used heroin | Test -) = ___________________________
(18 points)
6)
Assume that the probability that someone correctly completes a Maryland
tax return is 0.80. Suppose that 14 tax
returns are randomly selected. Round answers to 3 decimal places for each
question. Read the questions first.
succcess: ______________________________
n = ______
p = ______
a) What is the probability that exactly 10of the tax returns are correctly completed? ___________
b) What is the probability that at least 10 are correctly completed? ______________
c) What is the probability that 9or fewer are correctly completed? ______________
(7 points)
7) Assume that 53% of new companies are in business one year later.
Let x = number of new companies out of 100 which are in business one year later.
a) Find the mean and standard deviation of x.
m = ________________
s = ________________
b)
You are considering investing in a new industry. As a stock analyst you review 100 new
companies randomly selected from this industry. You find that 70 of these companies are in business one year
later. Is this an unusually low or
unusualy high number? You MUST justify and explain your answer.
First, find the
z-score for this value of x. ___________Round
to 2 decimal places.
Is this unusually low? ______ unusally high? ______ You MUST explain for credit.
(9 points)
8) Find the following probabilities for a random variable, z, which has the standard normal distribution. Round your answers to four decimal places.
a) P(–1.02 < z < –0.4) = ________________________
b) P( z > 1.89) = ________________________
c) P( z < –2.08) = ________________________
(24 points)
9)
IQ scores are normally distributed with mean = 100 and standard
deviation = 15. You may draw
diagrams for parts a) – d).
a) What percent of IQ scores are between 90 and 110? _____________
(First
round off the z-scores to 2 decimal places.
Secondly, round answer to 4 decimal places.)
z-scores: _______________
answer: ___________
b) What percent of IQ scores are less than 70? _____________
(First
round off the z-score to 2 decimal places.
Secondly, round answer to 4 decimal places.)
z-score: ______________
answer: ________________
c) What percent of the IQ scores are greater than 112? _________
(First
round off the z-score to 2 decimal places.
Secondly, round answer to 4 decimal places.)
z-score(s): ______________
answer: ________________
d) If an IQ is in the 85th percentile, what is the IQ?
Round off the z-score to 2 decimal places. Round off the answer to the nearest whole number.
_______________
-
CONTINUED -
Math153 TEST2 ANSWER KEY FORM A
Spring 2005
2a) 59C6 = 45,057,474 b) part d)
3a) 20/100 = .20
b) 90/900 = .10
c) RR = .2/.1 = 2
4) n= 4 Success: audited p = .12
P(x=2) = 4C2 (.12)2 (.88)2 = .0669
5) a) Assume that 10,000 people are tested. Complete the table below.
|
|
Test + |
Test - |
|
|
Has used heroin |
190 |
10 |
200 |
|
Has NOT used heroin |
392 |
9408 |
9800 |
|
|
582 |
9418 |
10,000 |
b) 190/582 = .3265
c) 9408/9418 = .9989
6) success: successful completion
n = 14
p = .8
a) .172
b) .172+.250+.250+.154+.044 = .870
c) .086 + .032 + .009 + .002 = .129
7) m = np = 100 (,53) = 53
s = 
= 
= 4.99 (or 4.990991885)
b) z = (70-53)/4.99 = 3.41
unusually low? NO unusually high? YES The z-score is greater than 2.
8)a) normalcdf(-1.02,-0.4) = .1907
b) normalcdf(1.89,10) = .0294
c) normalcdf(-10,-2.08) = .0188
9) a) z-scores: -.67, .67 c) z-score: .8
answer: .4971 = 49.71% answer: .2119 = 21.19%
b) z-score: -2 d) z = Invnorm(.85) = 1.04
answer = .0228 = 2.28% x = (1.04)(15)+100 = 115.6 or 116