Mr. Tuttle is planning to buy a new car. He’s considering the Ford Escape, a sport utility vehicle (SUV) that gets 28 highway miles per gallon, and the Ford Fusion, a mid-sized sedan that gets 31 highway miles per gallon. The mean fuel efficiency for all sport utility vehicles is 23, with a standard deviation of 7.6. The mean fuel efficiency of all mid-sized sedans is 27, with a standard deviation of 5.2. Which vehicle has a better gas mileage, relative to others of the same style?

The Ford Fusion sedan has a better gas mileage, because its z-score is greater.

The Ford Fusion sedan has a better gas mileage, because its z-score is closer to 0.

The Ford Escape SUV has a better gas mileage, because its z-score is greater.

The Ford Escape SUV has a better gas mileage, because its z-score is closer to 0.

Mr. Reiff is planning on buying a new car. He’s looking at the Ford Escape, a sport utility vehicle (SUV), which gets 28 highway miles per gallon, and the Ford Fusion, a mid-sized sedan, which gets 31 highway miles per gallon. The mean fuel efficiency for all sport utility vehicles is 23, with a standard deviation of 7.6. The mean of all mid-sized sedans is 27, with a standard deviation of 5.2. Which vehicle has a better standing, relative to others of the same style?

The Ford Fusion sedan has a better relative standing, because its z-score is greater.

The Ford Fusion sedan has a better relative standing, because its z-score is closer to 0.

The Ford Escape SUV has a better relative standing, because its z-score is greater.

The Ford Escape SUV has a better relative standing, because its z-score is closer to 0.

A machine in a potato chip factory is supposed to fill empty bags with approximately 10 ounces of potato chips. Unfortunately, the machine has been filling the bags with 2 extra ounces. This is a major problem for the company but was caught by an observant worker early in a shift. Here is the distribution of the amount of potato chips in the bags along with summary statistics for all bags with the extra 2 ounces. Which of the following correctly describes the distribution weights of the bags without the extra 2 ounces? Note that all values below are in ounces.

The shape would remain the same. Mean = 10. SD = 0.1.

The shape would become skewed to the left. Mean = 12. SD = -1.9.

The shape would become skewed to the left. Mean = 12. SD = 0.1.

The shape would remain the same. Mean = 10. SD = -1.9.

A plumber charges $40 to show up to a customer’s home and then $45 per hour. Here is the distribution along with summary statistics for the time spent (measured in hours) at jobs in the past week. The hours worked per job are to be converted to the dollar amount of money charged per job. Which of the following describes this new distribution? Note that all values below are in dollars.

The shape would remain the same. Mean = 161.50. SD = 94.50.

The shape would become skewed to the right. Mean = 121.50. SD = 2.10.

The shape would become skewed to the right. Mean = 161.50. SD = 94.50.

The shape would remain the same. Mean = 121.50. SD = 2.10.

The mean finish time for 48 racers who finished the grueling 50 km cross-country ski race at the Olympics is 2.164 hours and the standard deviation is 0.85 hours. The distribution of finish time is skewed to the right. What are the mean, standard deviation, and shape of the distribution of z-scores for these data?

mean = 0, standard deviation = 1, skewed to the right

mean = 0, standard deviation = 1, approximately normal

mean = 2.164, standard deviation = 0.85, skewed to the right

mean = 2.164, standard deviation = 0.85, approximately normal

Which of the following describes the relative positions of the mean and median for a probability distribution of a continuous random variable that is skewed to the left?

The median will be larger than the mean.

There is no way to determine the relative positions of the mean and median without the actual graph.

The mean and median will be equal.

The mean will be larger than the median.

Mrs. Trax regularly commutes between two cities. The normal curve shown models the distribution of her commute times.

mean 200; standard deviation 6.7

mean 100; standard deviation 6.7

mean 100; standard deviation 20

mean 200; standard deviation 10

Summative 2.1-2.3

Authored by Armina Wrice

Mathematics

12th Grade

CCSS covered

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OPEN ENDED QUESTION

3 mins • 2 pts

Molly Huddle, the fastest American in the race, broke the American record with a time of 30.22 minutes. Find and interpret Molly’s percentile.

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CCSS.HSS.IC.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Marielle Hall, another American in the race, had a time that was at the 91st percentile. What was her time?

29.71 min

29.99 min

32.65 min

32.66 min

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CCSS.HSS.ID.A.4

OPEN ENDED QUESTION

3 mins • 2 pts

The winner and world record breaker of the race was Almaz Ayana from Ethiopia. Find her z-score and interpret it in context.

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A homeowner was reading through a summary of his electric usage for the previous year. Typical high temperatures for each month were included in the summary and the teacher became curious about the distribution of those temperatures. Here are the data (measured in degrees Fahrenheit):
22 31 42 48 52 64 64 71 78 79 80 81
Which of the following is the correct calculation and interpretation of a percentile?

The month in which the typical high temperature was 48 degrees is at about the 25th percentile. This means that this month’s typical high temperature was less than about 25% of all months.

The month in which the typical high temperature was 79 degrees is at about the 16th percentile. This means that about 16% of the time the high temperature will be about 79 degrees.

The month in which the typical high temperature was 31 degrees is about at the 8th percentile. This means that about 8% of the time, the typical high temperature will be similar for this same month in the future.

The month in which the typical high temperature was 71 degrees is at about the 58th percentile. This means that this month’s typical high temperature was greater than about 58% of the other months.

OPEN ENDED QUESTION

3 mins • 2 pts

One of the bags of nuts weighed 15.1 ounces. Find the percentile for this bag of nuts. Interpret this value..

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OPEN ENDED QUESTION

3 mins • 1 pt

Calculate and interpret the standardized score for the bag of nuts that weighed 15.5 ounces.

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OPEN ENDED QUESTION

3 mins • 2 pts

The top competitor to We’re All Nuts, Inc. is URnuts.com. URnuts.com sells bags of mixed nuts that have a mean weight of 2 pounds and standard deviation 0.25 pounds. A customer purchased one bag of nuts from URnuts.com and found that it weighed 2.4 pounds.
Which bag of nuts has the more extreme weight, relatively speaking: A 15.5-ounce bag from We’re All Nuts or a 2.4-pound bag of nuts from URnuts.com?

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Summative 2.1-2.3

Molly Huddle, the fastest American in the race, broke the American record with a time of 30.22 minutes. Find and interpret Molly’s percentile.

Marielle Hall, another American in the race, had a time that was at the 91st percentile. What was her time?

The winner and world record breaker of the race was Almaz Ayana from Ethiopia. Find her z-score and interpret it in context.

One of the bags of nuts weighed 15.1 ounces. Find the percentile for this bag of nuts. Interpret this value..

Calculate and interpret the standardized score for the bag of nuts that weighed 15.5 ounces.

Estimate and interpret the median. Show your work by drawing lines on the cumulative relative frequency graph above.

Estimate the IQR. Show your work by drawing lines on the cumulative relative frequency graph above.

At what percentile was American Emily Infeld, with a time of 31.45 minutes? Interpret Emily’s percentile.

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