Statistics Module 3

Snowy Owls are known to have an average weight of 4.5 pounds. A parliament of snowy owls from the northeast part of the country has an average weight of 5.1 pounds per animal. Which of the following would be accurate?

• x̄ = 5.1

• μ = 5.1

x̄ = 5.1

Calculate the mean of the following: 32.5, 32.9, 30.8, 2.4, 38.4, 28.2, 31, 28.9, 39.9.

Round your answer to 4 decimal places.  

29.4444

Calculate the median of the following: 28, 2, 31, 17, 5, 13, 21, 24, 27, 19.

20

Calculate the mode of the following: 34, 26, 32, 33, 8, 17, 29, 31, 33, 4, 2, 14.

33

The table below shows the scores on an activity assignment for a section of MATH 2510. What was the mean score for that section? Round your answer to 4 decimal places

13.3871

Using the scores and grade weights below, what does the student need to score on the final exam to get an 80% in the class? Round your answer to 4 decimal places. 

65.6667

A company is looking at how many care packages their employees make per hour. The data is summarized below. What is the estimated mean number of care packages made per hour?

Round your answer to 4 decimal places.

11.2619

In order to estimate the length of wolves in a forest, 8 wolves are selected to be studied by some researches. The lengths of the wolves, in feet, are 4.72, 4.55, 3.51, 4, 4.6, 5.2, 5.88, 5.98. Find the variance of the lengths of the selected wolves. 

Round your answer to 4 decimal places.

0.7331

In order to find the lengths of wolves in a small animal preserve, all the wolves are measured, and their lengths, in feet, are 4.79, 4.85, 3.94, 5.94, 4.74, 5.11, 4.51, 5.71. Find the standard deviation of the lengths of the wolves in the entire animal preserve.

Round your answer to 4 decimal places. 

0.5997

Suppose you have a data set of size 9, with mean 40 and standard deviation 6. If you add two data points, both 21, to the data set, how will the mean and standard deviation change? 

The mean will decrease and the standard deviation will increase.

Suppose you have a data set of size 17, with mean 20 and standard deviation 3. If you add 3 to every data value, how will the mean and standard deviation change?

The mean will increase and the standard deviation will stay the same

Suppose you have a data set of size 12, with mean 30 and standard deviation 4. If you divide every data point by 2, how will the mean and standard deviation change?

The mean and standard deviation will both decrease

Fifteen amusement park visitors are randomly chosen, and the number of rides they were on are recorded. Choose the box-and-whisker plot that represents this data:

5, 4, 15, 12, 19, 16, 3, 10, 10, 12, 20, 15, 19, 8, 17

C

Calculate the 5-number summary for the following set of data:

2, 2, 3, 5, 7, 8, 9, 10, 10, 11, 16

Reminder: the 5-number summary includes the minimum, Q1, Median, Q3, Maximum

Also calculate the Interquartile Range

Minimum - 2

Q1 - 3

Median - 8 

Q3 - 10

Maximum - 16

Interquartile Range - 7 

Suppose you have a population with an unknown distribution with mean 40 and standard deviation 2. What is the smallest interval that is guaranteed to contain at least 99% of the population?

• 30.58 < x < 49.42 

• 36.00 < x < 44.00

• 39.00 < x < 41.00

• 20.00 < x < 60.00

• 36.08 < x < 43.92

20.00 < x < 60.00

Find the expected value of the following probability distribution. Round your answer to 2 decimal places.

3.54

Find the missing value of the following probability distribution:

0.64

For the following probability distribution, compute P(x<3)

0.31

For the following probability distribution, compute P(x <=2)

0.52

For the following probability distribution, compute P(x=3 | x≤4). Round your answers to 4 decimal places.

0.141

For each of the following situations, determine if you could calculate the probability using the binomial distribution. If you cannot, choose the reason why.

1. You have an urn containing 3 white balls, 4 green balls, and 8 orange balls. You draw 3 balls, one at a time, with replacement. What is the probability that none of the three balls are orange?

2. You have an urn containing 3 white balls, 4 green balls, and 8 orange balls. You draw 3 balls, one at a time, with replacement. What is the probability that the three balls are all different colors?

3. You have an urn containing 3 white balls, 4 green balls, and 8 orange balls. You draw 3 balls, one at a time, with replacement. What is the probability that two are white and one green?

4. You have an urn containing 3 white balls, 4 green balls, and 8 orange balls. You draw 3 balls, one at a time, with replacement. What is the probability that at least one ball is not green?

5. You have an urn containing 3 white balls, 4 green balls, and 8 orange balls. You draw 3 balls, one at a time, without replacement. What is the probability that the three balls are all white?

1. The situation is binomial.

2. The situation is not binomial since there are more than two possible outcomes.

3. The situation is not binomial since there are more than two possible outcomes.

4. The situation is binomial.

5. The situation is not binomial since the trials are not independent.

A staple gun misfires 25% of the time, the rest of the time it staples correctly. If I try to staple something 20 times and letting r represent the number of times the stapler misfires, what would be the correct notation to indicate the probability that exactly 5 of those times the stapler misfires?

• P(r=5)

• P(r<5)

• P(r>=5)

• P(r>5)

• P(r<=5)

P(r=5)

Consider a binomial experiment with n = 33 trials and the probability of success on each trial is p = 19%. Compute the probability of exactly 6 successes.

Round your answer to 4 decimal places.

0.1762

An earth-conscious clothing store offers a 15% discount if you bring in a bag full of old clothing to recycle the fabric. The probability that each bag brought in will contain fabric that can actually be recycled is 69%. In a given day, if there are 18 bags of fabric brought in to recycle, calculate the following:

Round each answer to 4 decimal places.

1. The probability that more than 15 bags will contain fabric that can be recycled

2. The probability that fewer than 13 bags will contain fabric that can be recycled

3. The probability that at most 11 bags will contain fabric that can be recycled

4. The probability that at least 9 bags will contain fabric that can be recycled

1. 0.0502

2. 0.5029

3. 0.3111

4. 0.9736

In a newly released murder mystery, the author decides to secretly print two different versions of the book with different endings. In 1 out of every 8 books, the butler is the murderer. Suppose 7 friends each buy a copy of the book. Find the probability of each of the following events occurring:

Round each answer to 4 decimal places.

1. At least 4 read that the butler did it:

2. More than 2 read that the butler did it:

3. No more than 1 read that the butler did it:

4. Fewer than 3 read that the butler did it:

1. 0.0062

2. 0.0463

3. 0.7854

4. 0.9537

A candy manufacturer has replaced 5.17% of their chocolate bars with a new mystery flavor. Find the mean and standard deviation for the number of mystery bars in a random sample of 303 candy bars.

Round your answers to 4 decimal places.

Mean - 15.6651

SD - 3.8542

If we flip a coin 100 times and get heads 40 times, we would expect that our coin is unfair, landing heads about 40% of the time.  Which of the following would support this line of reasoning? 

• Central Limit Theorem

• The Empirical Rule

• Law of Large Numbers

• Chebyshev’s Thorem 

• Law of Large Numbers

Assume approximately 11% of all people are left-handed.  If you select a group of 207 people, what is the expected value of those selected that are left handed?

Round your answers to 2 decimal places. 

22.77

Find the mean of the following:

67, 50, 60, 3, 14, 16, 3, 53, 17, 37, 7 

Round your answer to 4 decimal places. 

29.7273

Find the median of the following:

14, 48, 34, 5, 47, 33, 7, 54, 36, 14

Round your answer to 1 decimal place.

33.5

Consider the following semester grades. What is this student's term GPA?  

Round your answer to 4 decimal places. 

2.7765

Suppose you have a data set of size 40, with mean 34 and standard deviation 5. If you add two data points, both 34, to the data set, how will the mean and standard deviation change?

Mean will stay the same 

SD will decrease 

Suppose you have a data set of size 40, with mean 34 and standard deviation 5. If you add two data points, both 15, to the data set, how will the mean and standard deviation change?

Mean will decrease

SD will increase

For a given data set, we would expect approximately 25% of the data to fall between the maximum and what other value?

Upper Quartile

My brother's trick coin lands on heads 24% of the time. If I flip it 47 times what is the probability that I will get exactly 17 heads?

Round your answer to 4 decimal places.

0.0212

An assembly line machine produces a defective widget 16% of the time, the rest of the time it produces a widget correctly. If the assembly line produces 42 widgets, compute the probability that at least 4 of those widgets are defective?

Round your answer to 4 decimal places.

0.921

Suppose a Binomial random variable has a 0.29 probability of success on a single trial.  What is the expected value when performing 70 trials?

Round your answer to 2 decimal places. 

20.3

A tire repair shop is able to patch 75% of air leaks. When the repair shop is unable to patch a leak, they have to replace the tire. If 20 tires are brought in with an air leak and r represents the number of tires that can be patched, what would be the correct notation to indicate the probability that at least 5 of the tires are able to be patched?

• P(r<5)

• P(r=5)

• P(r<=5)

• P(r>5)

• P(r>=5)

P(r>=5)

Find the missing value of the following probability distribution:

0.52

What is the expected value for this probability distribution?

10.25

What is the standard deviation for this probability distribution? Round your answer to 4 decimal places.

5.4675

At a carnival game you are able to randomly select two rubber ducks from a kiddie pool (without replacement). The pool contains 19 marked ducks and 28 that are not marked.

Let x represent the number of marked ducks selected. Calculate the expected value of x.

Hint: it may be helpful to fill in the following table: 

Round your answer to 4 decimal places.

0.8085

Suppose you have a data set of size 13 with no repeated values, and that the mean and median are both 18.

1. If you remove the smallest value and largest value from the data set, how will the mean and median change?

2. If you remove the two largest values from the data set, how will the mean and median change?

3. If you remove the value 18 from the data set, how will the mean and median change?

1. The change in mean cannot be determined; the median will stay the same 

2. The mean will decrease; the median will decrease

3. The mean will stay the same; the change in medica cannot be determined

For each of the following situations, determine if you could calculate the probability using the binomial distribution. If you cannot, choose the reason why.

1. You have one bag of hard candy, containing 6 Lemon, 3 Orange, and 4 Cherry flavors. You reach in and draw three candies, one at a time, and set them aside after each draw.  Find the probability that none of the candies are Lemon.

2. You have three bags of hard candy, each containing 6 Lemon, 3 Orange, and 4 Cherry flavors.  You draw one candy from each bag and set it aside.  Find the probability that two candies are Cherry and one is Lemon.

1. The situation is not binomial since the trials are not independent

2. The situation is not binomial since there are more than two possible outcomes.