# 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

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.

hit(s) in his next

7

at bats?

Express your answer as a decimal to at least 4 decimal places.

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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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