## (Solved) PRINTABLE VERSION Practice Test 4 Question 1 Given P(Ec ) = 0.43, P(F) = 0.54, and P(E F) = 0.18. Find P( E | Fc ). a) 0.9069 b) 0.7222 c) 0.8478 d)

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Practice Test 4
Question 1
Given P(Ec ) = 0.43, P(F) = 0.54, and P(E F) = 0.18. Find P( E | Fc ).
a) 0.9069 b) 0.7222 c) 0.8478 d) 0.3333 e) 0.5200 f) None of the above. Question 2
Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the
probability that the first card drawn is a Diamond and the second card drawn is not a Diamond?
a) 0.7500 b) 0.0577 c) 0.1875 d) 0.1912 e) 0.0588 f) None of the above. Question 3
A pair of fair dice is cast. What is the probabiliy that at least one of the numbers falling uppermost is a 1,
given that the sum of the numbers falling uppermost is even?
a) 0.3667 b) 0.2778 c) 0.1389 d) 0.4545 e) 0.3056 f) None of the above. Question 4
5 black balls and 8 white balls are placed in an urn. Two balls are then drawn in succession. What is the
probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first
ball?
a) 0.5680 b) 0.3590 c) 0.6154 d) 0.2051 e) 0.2564 f) None of the above. Question 5
Urn A contains 12 yellow balls and 5 red balls. Urn B contains 7 yellow balls and 7 red balls. Urn C
contains 5 yellow balls and 6 red balls. An urn is picked randomly (assume that each urn is equally likely
to be chosen), and then a ball is picked from the selected urn. What is the probability that the chosen ball
came from urn B, given that it was a yellow ball?
a) 0.3011 b) 0.4251 c) 0.0692 d) 0.2738 e) 0.0639 f) None of the above. Question 6 John is interested in purchasing a multi-office building containing five offices. The current owner
provides the following probability distribution indicating the probability that the given number of offices
will be leased each year.
Number of Lease Offices 0
1
2
3
4
5
Probability
5/29 4/29 2/29 10/29 7/29 1/29
If each yearly lease is \$12,000, how much could John expect to collect in yearly leases for the whole
building in a given year?(in dollars)
a) E(X) = \$29,399.31 b) E(X) = \$29,299.31 c) E(X) = \$29,449.31 d) E(X) = \$29,379.31 e) E(X) = \$29,409.31 f) None of the above. Question 7
A probability distribution has a mean of 28 and a standard deviation of 4. Use Chebychev's inequality to
estimate the probability that an outcome of the experiment lies between 20 and 36.
a) 0.5000 b) 0.7500 c) 0.0204 d) 0.9796 e) 0.2500 f) None of the above. Question 8
If the racetrack publishes that the odds in favor of a horse winning a race are 4 to 6, what is probability
that the horse will not win the race?
a) 0.0417 b) 0.2500 c) 0.1667 d) 0.4000 e) 0.6000 f) None of the above. Question 9
The probability distribution of a random variable X is given below.
x
1 2 3
4
9
P(X = x) 1/8 1/3 1/24 5/24 7/24
Given the following mean
Find the variance (Var(X)) and the standard deviation, respectively.
a) [63.20, 7.95] b) [691.00, 26.29] c) [40.48, 6.36] d) [1742.76, 41.75] e) [9.65, 3.11] f) None of the above. Question 10
Consider the following Binomial Experiment: The probability that a cell phone manufactured at
Electronics Unlimited is defective is 0.11. If a sample of 8 cell phones is selected at random, what is the
probability that at least one is defective?
a) 0.5577 b) 0.4423 c) 0.6063 d) 0.3937 e) 0.3504 f) None of the above. Question 11
Consider the following binomial experiment: A survey shows 72% of households in Centercity own a
DVD player. In a random sample of 20 households in this city, what is the probability that exactly 8
households own a DVD player?
a) 0.0025 b) 0.0023 c) 0.0021 d) 0.0024 e) 0.0017 f) None of the above. Question 12
Consider the following binomial experiment: A newspaper publisher claims that 50% of the people in a
certain community read his newspaper. Doubting the assertion, a competitor randomly surveys 236
people in the community. Find the standard deviation of this experiment, if the newspaper publisher's
claim is correct.
a) 8.0811 b) 7.4811 c) 7.6811 d) 7.9811 e) 7.8811 f) None of the above. Question 13
Let Z be a standard normal variable. Find P(Z &lt; -1.37). a) 0.0968 b) 0.9147 c) 0.9032 d) 0.0869 e) 0.0853 f) None of the above. Question 14
Let Z be a standard normal variable. Find P(1.21 &lt; Z &lt; 3.00).
a) 0.8875 b) 0.1574 c) 0.1138 d) 0.8836 e) 0.1118 f) None of the above. Question 15
Let Z be a standard normal variable. Find the value of z if z satisfies P( -z &lt; Z &lt; z) = 0.3616.
a) -0.35 b) 0.40 c) 0.47 d) 0.30 e) 0.48 f) None of the above. Question 16 Let Z be a standard normal variable. Find the value of z if z satisfies P( Z &lt; z) = 0.0052.
a) -2.50 b) 0.05 c) 2.55 d) -1.50 e) -2.56 f) None of the above. Question 17
Suppose X is a normal random variable with and
Find P(3.6 &lt; X &lt; 53.5).
a)
b)
c)
d)
e)
f) None of the above. Question 18
Laboratory experiment shows that the life of the average butterfly is normally distributed with a mean of
18.8 days and a standard deviation of 2 days. Find the probability that a butterfly will live between 12.88
and 15.76 days.
a) 0.0653 b) 0.0628 c) 0.0639 d) 0.0636 e) 0.0649 f) None of the above. Question 19
Use the normal distribution to approximate the following binomial distribution. You claim that 73% of
the voters in your district will vote for you. If the district has 350 voters, what is the probability that at
least 274 will actually vote for you?
a)
b)
c)
d)
e)
f) None of the above. Question 20
Use the normal distribution to approximate the following binomial distribution: A convenience store
owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee
during their visit. A random sample of 35 customers is made. If the store owner's claim is correct, what
is the probability that fewer than 24 customers in the sample buy coffee during their visit on that certain
day of the week?
a)
b)
c) d)
e)
f) None of the above.

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