1. Jeopardy Final Jeopardy Z-Nation Percentiles Ring My Bell Potpourri
What’s My
Line?
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Final Jeopardy

2. 1 - $100
Suppose the scores on an exam have a mean of 75 with a standard deviation of 8. If one student has a test result with a z-score of -1.5, and a second student has a test result with a z-score of 2.0, how many points higher was the second student’s result than the first?
Student 1 made a 63, student 2 made a 91. So, 91 – 63 = 28 points higher.

3. 1 - $200
Suppose the average score on a national exam is 500 with a standard deviation of 100. If each score is increased by 20 points and the result is increased by 10%, what are the new mean and standard deviation?
Mean: 572
Standard Deviation: 110

4. 1 - $300
Gina’s doctor told her that the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is Interpret this z-score.
Gina’s systolic blood pressure is 1.5 standard deviations above the mean for other women her age.

5. 1 - $400
At a college the scores on the Physics final exam are approximately normally distributed, with a mean of 72 and a standard deviation of 10. The scores on the Linear Algebra final exam are also approximately normally distributed with a mean of 76 and a standard deviation of 7. A student enrolled in both classes scored an 83 in Physics and an 82 in Linear Algebra. Relative to the students in each respective class, in which subject did this student do better?
Physics (zP =1.1, zLA = .857)

6. 1 - $500
The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10% of loaves weighed less than ounces, and 20% weighed more than ounces. What are the mean and standard deviation of the distribution of the weights of the loaves of bread?

7. 2 - $100
The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Joyce is at the 99th percentile in height for adult women, then her height, in inches, is closest to
60 D) 70
62 E) 74 68
D: 70 inches

8. 2 - $200
Suppose fastball speeds in collegiate baseball are normally distributed with a mean of 86mph and a standard deviation of 4mph. Suppose further that major league scouts will only consider pitching prospects who can throw a fastball at least 90mph. What percentage of the pitching prospects who are considered can throw at speeds over 95 mph?
7.7% or .077

9. 2 - $300
Assuming that heights of professional male tennis players follow a bell-shaped distribution, arrange in ascending order:
A height with a z-score of 1
A height with a percentile rank of 80%
A height at the third quartile (Q3)
III (75%), II (80%), I (84%)

10. 2 - $500
A factory dumps a mean of 2.43 tons with a standard deviation of 0.88 tons of pollutants into a river each week. Calculate the 85th percentile.
3.34 tons

11. 2 - $400
A trucking firm determines that its fleet of trucks averages 12.4 mpg with a standard deviation of 1.2 mpg on cross-country hauls. Find the IQR for this company.
Q1 = 11.6, Q3 = 13.2,
IQR = = 1.6 mpg

12. 3 - $100
The mean income per household in a certain state is $9500 with a standard deviation of $1750. About 95% of household incomes are between what two values?
Using the % rule: 6000 and Using exact values: 6070 and

13. 3 - $200
Which is the best estimate of the standard deviation of the given distribution?
A) B) C) D) E) 60
B: 10

14. 3 - $300
Which curve has the larger mean and which has the larger standard deviation?
A B
A has a the larger standard deviation, B has the larger mean

15. 3 - $400
You make a histogram of your data to check the nearly normal condition. It could go either way. You next check the normal probability plot. The result is a curved shape. Do you have approximately normal data? Explain why or why not.
No, to be approximately normal, the normal probability plot should produce a relatively linear graph.

16. 3 - $500
A company produces movie trailers with a mean of 150 seconds and a standard deviation of 40 seconds. Using the % rule, what percent of movie trailers lies between 1 and 2 standard deviations below the mean?
About 13.5%

17. 4 - $100 A

18. 4 - $200
The time required for the first stage of an assembly line is normally distributed with a mean of 28 minutes and a standard deviation of 4 minutes. What is the probability that it will take a product more than 30 minutes to get through the first stage of the assembly line?
.309 or 30.9%

19. 4 - $300
In a particular neighborhood in 2010 homes sold for a mean of $225,000 with a standard deviation of $20,000. Over the course of the last seven years, the price of homes has increased by 15%. What are the new mean and standard deviation?
Mean: $258,750, Standard deviation: $23,000

20. 4 - $400
The average noise level in a restaurant is 30 decibels with a standard deviation of 4 decibels. 99% of the time the noise level is below what value?
39.3 decibels

21. 4 - $500
An electronic product takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hour, what is the probability that an item will take between 3 and 4 hours?
.673 or 67.3%

22. 5 - $100 Just a small town girl… living in a lonely world
she took the midnight train going anywhere

23. 5 - $200 Kiki do you love me? Are you riding?
Say you’ll never ever leave from beside me

24. 5 - $300 Never gonna give you up, Never gonna let you down…
Never gonna run around and dessert you.

25. 5 - $400 It’s gonna take a lot to drag me away from you…
There’s nothing that a hundred men or more could ever do

26. 5 - $500 Sleight of hand and twist of fate,
On a bed of nails she makes me wait…
And I wait, without you

27. Final Jeopardy
Trains carry bauxite ore from a mine in Canada to an aluminum processing plant in northern New York state in hopper cars. Filling equipment is used to load ore into hopper cars. When functioning properly, the actual weights of ore loaded into each car by the filling equipment at the mine are approximately normally distributed with a mean of 70 tons and a standard deviation of 0.9 ton. If the mean is greater than 70 tons, the loading mechanism is overfilling.
If the filling equipment is functioning properly, what is the probability that the weight of the ore in a randomly selected car will be 70.7 tons or more? Show work.
Suppose that the weight of ore in a randomly selected car is 70.7 tons. Would that fact make you suspect that the loading mechanism is overfilling the cars? Justify your answer.