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Some Practice Problems from Exam 1, Spring 2014
(Questions 1-5)
The histogram and boxplot show the daily returns (in percent) of Facebook Stock from 1/2013 to 2/2014 for a total
282 days. All return values were unique so there were no multiple days with the same return value.
(1) Without the two large outliers, the shape of the return distribution is approximately:
A) Left skewed
B) Right skewed
C) Bell-shaped
D) Bimodal
E) Extreme
(2) The median of the data is approximately:
A) -2.0
B) -1.5
C) 0
D) 1.5
E) 2.0
(3) The IQR of the data is approximately:
A) 0
B) 0.5
C) 1.0
D) 2.0
E) 3.0
(4) About what percentage of the data were below the return value of 10%?
A) 99
B) 75
C) 50
D) 25
E) 1
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(5) The mean of the data is 0.3%. Suppose the largest data value is removed. The new mean is approximately:
A) 0
B) 0.2
C) 0.3
D) 0.4
E) 0.5
(Questions 6-9)
A randomly selected email has a 0.90 probability of being spam. It has been estimated that given a message is
spam, the probability that the word “Replica” is in it is 0.80. We also know that given a message is not spam, there
is 0.10 probability that the email has the word “Replica”.
(6) What is the probability a randomly selected email is not spam?
A) 0.05
B) 0.10
C) 0.20
D) 0.72
E) 0.80
(7) What is the probability a randomly selected email contains the world “Replica”?
A) 0.99
B) 0.90
C) 0.80
D) 0.73
E) 0.72
(8) What is the probability a randomly selected email is spam and contains the word “Replica”?
A) 0.99
B) 0.90
C) 0.80
D) 0.73
E) 0.72
(9) You get a message with the word “Replica” in it. What is the probability that this message is spam?
A) 0.720
B) 0.889
C) 0.910
D) 0.986
E) 0.997
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(Questions 10-14)
A recently installed assembly line has problems with intermittent breakdowns. It seems that the equipment fails at
some point during 20% of the eight-hour shifts that the plant operates. Each day contains three consecutive shifts.
Assume that the failure events during the shifts are independent.
(10) What is the probability that the assembly line works fine throughout the three shifts on Monday?
A) 0.13
B) 0.20
C) 0.51
D) 0.80
E) 0.92
(11) What is the probability that the assembly line works fine on Monday but breaks down during the first shift on
Tuesday?
A) 0.03
B) 0.04
C) 0.08
D) 0.10
E) 0.20
(12) What is the probability that the assembly line breaks down on a given day?
A) 0.49
B) 0.63
C) 0.72
D) 0.80
E) 0.97
(13) What is the probability that the assembly line breaks during only one shift during a chosen day?
A) 0.10
B) 0.16
C) 0.20
D) 0.38
E) 0.54
(14) Given that the assembly line broke down during the first and second shifts, what is the probability that it will
break down during the third shift?
A) 0.13
B) 0.20
C) 0.51
D) 0.80
E) 1.00
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(Questions 15-19)
Let X = gas price (dollars per gallon) at a randomly selected gas station in a certain region. It is known that X is
normally distributed with a mean $3.50 and a standard deviation of $0.20.
(15) A gas station is selected at random. What is the probability that the price at this station is less than $3.50?
A) 0.00
B) 0.34
C) 0.48
D) 0.50
E) 0.68
(16) A randomly selected gas station’s price is found to be $3.30. What is the z score for this station’s gas price?
A) -1.00
B) -0.20
C) 1.00
D) 3.30
E) 3.40
(17) A gas station is selected at random. What is the probability that the price at this station is less than $3.30?
A) 0.68
B) 0.48
C) 0.34
D) 0.25
E) 0.16
(18) What is the probability that a randomly selected gas station has a price between $3.10 and $3.70?
A) 0.51
B) 0.48
C) 0.68
D) 0.82
E) 0.95
(19) What is probability that a randomly selected gas station has a price between $3.10 and $3.70 given that its
price is at least $3.50?
A) 0.51
B) 0.48
C) 0.68
D) 0.82
E) 0.95
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(Questions 20-24)
X is a uniform random variable on [-5,5].
Consider the following events:
A={X>0}
B={X<0}
C={X=0}
D={X≠0}
(20) Events A and B are both:
A) Independent and mutually exclusive
B) Independent and complementary
C) Dependent and mutually exclusive
D) Dependent and complementary
E) None of the above
(21) P(C) is:
A) 0
B) 1/10
C) 1/5
D) 1/2
E) 1
(22) P(D) is:
A) 0
B) 1/10
C) 1/5
D) 1/2
E) 1
(23) P(C and D) is:
A) 0
B) 1/10
C) 1/5
D) 1/2
E) 1
(24) Events C and D are both:
A) Dependent and mutually exclusive
B) Dependent and complementary
C) Independent and complementary
D) Independent and dependent
E) None of the above
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(Questions 25-29)
The credit manager of a large department store claims that the mean balance for the store’s charge account
customers is $800. An auditor thinks that the mean balance should be higher than what the credit manager claims.
The auditor selects a random sample of 101 accounts and finds a mean balance of $810 and a standard deviation of
$200. The auditor will only examine all charge account balances if the data provide evidence in support of his – the
auditor’s - view. Let μ = mean balance of all customer accounts. Set α = 0.05.
(25) Choose the correct test:
A) H0: μ ≥ 800 vs Ha: μ < 800
B) H0: μ > 800 vs Ha: μ ≤ 800
C) H0: μ ≤ 800 vs Ha: μ > 800
D) H0: μ < 800 vs Ha: μ ≥ 800
E) H0: μ = 800 vs Ha: μ ≠ 800
(26) Based on the random sample, what is an estimate of μ?
A) 800
B) 810
C) 1010
D) 1000
E) 805
(27) What is the value of the test statistic?
A) 0.50
B) 0.40
C) 1.00
D) 2.00
E) 2.50
(28) What is the distribution of the test statistic if we assume null hypothesis is true?
A) Normal with mean zero and standard deviation 1
B) Normal with mean 800 and standard deviation 200
C) Normal with mean 825 and standard deviation 200
D) t distribution with degrees of freedom equal to 80
E) t distribution with degrees of freedom equal to 100
(29) Based on the results of the hypothesis test, what should be the auditor’s final conclusion and action?
A) There is a statistically significant result. All the accounts should be examined.
B) There is a statistically significant result. All the accounts should not be examined.
C) There is no statistically significant result. All the accounts should be examined.
D) There is no statistically significant result. All the accounts should not be examined.
E) None of the above
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(Questions 30-34)
A survey conducted recently by the American Bankers Association found that 78 out of 300 banks expected to
acquire another bank within 5 years. Let: p = population proportion of American banks that expected to acquire
another bank within 5 years. We would like to conduct the following hypothesis test:
H0: p ≤ 0.35
Ha: p > 0.35
Let α = 0.05.
(30) An estimate of p is:
A) 0.05
B) 0.26
C) 0.35
D) 0.65
E) 0.74
(31) Assuming the null hypothesis is true, what is standard error of the estimate of p?
A) 0.0253
B) 0.0275
C) 0.0289
D) 0.0500
E) 0.0548
(32) Assuming the null hypothesis is true, what is the value of the test statistics?
A) 3.6
B) 3.0
C) 3.3
D) -3.0
E) -3.3
(33) Assuming the null hypothesis is true, what is the distribution of the test statistics?
A) Normal with mean 0, and standard deviation of 1.
B) Normal with mean 0.26, and standard deviation of 1.
C) Normal with mean 0.35, and standard deviation of 1.
D) Normal with mean 0.64, and standard deviation of 1.
E) Normal with mean 0.74, and standard deviation of 1.
(34) What is the p-value approximately equal to? What would be your decision?
A) P-value ≈ 0.00, reject the H0.
B) P-value < 0.05, reject the H0.
C) P-value ≈ 0.05, test is inconclusive.
D) P-value ≈ 0.50, fail to reject H0.
E) P-value ≈ 1.00, fail to reject H0.
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(Questions 35-37)
The Federal Aviation Administration told airlines to assume that passengers average 190 pounds with a standard
deviation of 35 pounds. (The weights include clothing and carry-on baggage.) The airlines can assume that 190
pounds is the population mean weight of the passengers, and 35 pounds is the population standard deviation of the
passengers.
(35) Suppose a passenger is selected at random. What is the probability that this passenger weighs at least 190
pounds?
A) 0.32
B) 0.50
C) 0.68
D) 0.95
E) Can’t be determined.
(36) Suppose 100 passengers board a plane. Consider the 100 passengers as a random sample from the larger
population of passengers. What is the approximate probability that the mean weight of these passengers is at least
193.5 pounds?
A) 0.16
B) 0.32
C) 0.50
D) 0.68
E) 0.95
(37) Continuing with question (32), what is the approximate probability that the total weight of these passengers is
at least 18300 pounds?
A) 0.500
B) 0.680
C) 0.840
D) 0.950
E) 0.975
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