Cameron University Statistics Questions

3/14/22, 7:50 AMMyOpenMath
Chapter 5 HW
Joao Guilherme Guercheski Duleba
Question 1
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A small regional carrier accepted 15 reservations for a particular flight with 12 seats. 10 reservations
went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for
the flight with a 41% chance, independently of each other.
Find the probability that overbooking occurs.
Find the probability that the flight has empty seats.
Question 2
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About 24% of flights departing from New York’s John F. Kennedy International Airport were delayed in
2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested
in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one
flight is delayed, the next flight is more likely to be delayed, which of the following statements is
correct?
We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this
probability.
We cannot calculate this probability using the binomial distribution since whether or not one
flight is delayed is not independent of another.
We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this
probability.
We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this
probability.
Question 3
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Suppose that a box contains 7 cameras and that 4 of them are defective. A sample of 2 cameras is
selected at random without replacement. Define the random variable X as the number of defective
cameras in the sample.
Write the probability distribution for
k
P(X
= k
X
.
)
What is the expected value of
X
?
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Question 4
A baseball player has a batting average of
0.375
What is the probability that he has exactly
5
0/1 pt
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.
hit(s) in his next
7
at bats?
Express your answer as a decimal to at least 4 decimal places.
Question Help:
Video
Question 5
A binomial experiment consists of 20 trials. The probability of success on trial 13 is 0.26. What is the
probability of success on trial 17?
0.63
0.65
0.89
0.35
0.26
0.53
Question 6
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According to the American Red Cross, 9.4% of all Connecticut residents have Type B blood. A random
sample of 19 Connecticut residents is taken.
X =
the number of CT residents that have Type B blood, of the 19 sampled.
What is the expected value of the random variable
X
?
1.729 2.014 1.786 2.128 1.881 2.28
Question 7
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According to the American Red Cross, 10.8% of all Connecticut residents have Type B blood. A random
sample of 18 Connecticut residents is taken.
X =
the number of CT residents that have Type B blood, of the 18 sampled.
What is the standard deviation of the random variable
X
?
√1.488942
√1.734048
√1.384992
√1.9008
√1.845792
√1.804158
Question 8
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When dragons on planet Dathomir lay eggs, the eggs are either green or yellow. The biologists have
observed over the years that 22% of the eggs are yellow, and the rest green. Next spring, the lead
scientist has permission to randomly select 68 of the dragon eggs to incubate. Consider all the possible
samples of 68 dragon eggs.
What is the mean (μ) number of yellow eggs in samples of 68 eggs?
μ=
(Please show your answer to 1 decimal place)
What is the standard deviation (σ) in the number of yellow eggs in samples of size 68?
σ=
(Please show your answer to 1 decimal place)
Question 9
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Assume Binomial Distribution with n = 13 and p = 0.6. Please show your answers to 4 decimal places.
P(X `=` 6) =
P(X `=` 6) =
Question 10
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The television show 50 Minutes has been successful for many years. That show recently had a share of
27, meaning that among the TV sets in use, 27% were tuned to 50 Minutes. Assume that an advertiser
wants to verify that 27% share value by conducting its own survey, and a pilot survey begins with 11
households have TV sets in use at the time of a 50 Minutes broadcast. Please show your answer to 4
decimal places.
Find the probability that none of the households are tuned to 50 Minutes.
P(none) =
Find the probability that at least one household is tuned to 50 Minutes.
P(at least one) =
Find the probability that at most one household is tuned to 50 Minutes.
P(at most one) =
If at most one household is tuned to 50 Minutes, does it appear that the 27% share value is wrong? (Hint:
Is the occurrence of at most one household tuned to 50 Minutes unusual?)
no, it is not wrong
yes, it is wrong
Question 11
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A pharmaceutical company receives large shipments of ibuprofen tablets and uses this acceptance
sampling plan: randomly select and test 24 tablets, then accept the whole batch if there is at most one
that doesn’t meet the required specifications. If a particular shipment of thousands of ibuprofen tablets
actually has a 10% rate of defects, what is the probability that this whole shipment will be accepted?
P(accept shipment) =
Question 12
((Please show your answer to 4 decimal places)
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A court stenographer makes three typographical errors per hour on average. Find the probability that
(a) The stenographer makes exactly seven typographical errors during an hour long court case.
(b) The stenographer makes no more than two typographical errors during an hour long court case.
(c) The stenographer makes six or more typographical errors during an hour long court case.
Round all answers to four decimal places.
Question 13
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Occasionally an airline will lose a bag. A small airline has found it loses an average of 6.9 bags each day.
Find the probability that, on a given day,
(a) The airline looses exactly sixteen bags.
(b) The airline looses fewer than four bags.
(c) The airline looses more than thirteen bags.
Round all answers to four decimal places.
Question 14
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The Poisson Distribution
The Poisson Distribution is a Discrete Probability Distribution that is commonly applied when a series
of trials/experiments occur over an interval. (The number of meteors per hour; hailstones per acre).
Here, the average time/distance/etc. between each event must be known.
This type of distribution may be used if the following conditions apply:
Each event is independent.
The average rate is constant (events per interval).
Two events cannot occur at the same time.
Apply the Poisson Distribution to a scenario.
On average, a baking student accidentally drops three pieces of egg shell into the batter of every two
cakes made.
The conditions of a Poisson Distribution are met:
The baking of a cake does not affect the outcome of any other cake. (independent events)
The average rate is constant: 3 pieces per 2 cakes `(rate = 3/2 = 1.5)`
Baking (and dropping eggshells) is a sequential process. (Two events cannot occur at the same time)
Use the scenario above to determine the expected value (`mu`) and selected probabilities below. You
may wish to use the Poisson Distribution Calculator hosted by the University of Iowa’s Department of
Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used
in class. (link: Poisson Distribution Calculator )
a. On average, how many egg shells do you expect to be in a single cake?
`mu = `
(decimal answers only)
b. If a single cake is bought, what is the probability of finding 0 egg shell pieces in it?
`P(X = 0) = `
(include four decimal places)
c. If a single cake is bought, what is the probability of finding more than two egg shell pieces in it?
`P(X > 2) = `
(include four decimal places)
Question 15
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A bag contains 9 Cherry Starbursts and 21 other flavored Starburts. 8 Starbursts are chosen randomly
without replacement.
Find the probability that 4 of the Starbursts drawn are cherry.
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Question 16
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A bag contains 11 $50 bills and 55 $1 bills. 20 bills are drawn without replacement.
Find the probability that 4 of the bills drawn are $50s.
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