Statistical Reasoning Unit 2 Summative Assessment

Which of the following examples would NOT be able to be described by a normal curve?

• The height of the actresses on Broadway

• Rolling two dice, 50 times, and observing the sum of the two dice

• How many ounces of sugar in a 20 oz container

• The shoe size of all the students in the school

In a rural part of the state, the distance to the local hospital varies according to a normal distribution, with a mean of 10.5 miles and a standard deviation of 3 miles. The graph below shows the distribution.

According to the Empirical rule, what percentage of houses are between 4.5 miles and 13.5 miles away from the

hospital?

• 47.5%

• 84%

• 81.5%

• 50%

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The amount of weight a freshman college student gains when they attend a four-year college varies according to a normal distribution, with a mean of 2.5 lbs and a standard deviation of 10.8 lbs. If a college student lost 4 pounds, find and interpret their z-score.

• Their z-score of -0.602 says that they lost -0.602 standard deviations below the mean weight.

• Their z-score of -0.602 says that they were 0.602 standard deviations below the mean weight gain of 2.5 lbs.

• Their z-score of 0.139 says that they lost 0.139 standard deviations of weight.

• Their z-score of 0.602 says that they were 0.602 standard deviations above the mean weight loss of 2.5 lbs.

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Professor Kimmy administers two versions of the MATH 101 final exam, both covering the same

content but within different context and numbers. Version A had a standard deviation of 7 and a mean score of 78. Version B had a mean score of 83 with a standard deviation of 5.8.

Elijah got an 83 on Version A and Tanya took Version B earning an 87. Which of the following statements is true?

• Tanya did better on the final exam because her score of 87 is higher than Elijah’s score of 83.

• Elijah did better on the final exam because his standardized score of 0.71 is higher than Tanya’s

  standardized score of 0.69.

• Tanya did better on the final exam because her standardized score of 1.29 is higher than Elijah’s

  standardized score of 0.

• Elijah did better on the final exam because his standardized score in the 71st percentile is higher than Tanya’s standardized score in the 69th percentile.

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The heights of NFL football players are approximately normally distributed with a mean of 71.5 inches and a standard deviation of 2.3 inches. Aaron Rogers is 6 feet 2 inches. What percentile does that place him at?

• 43rd

• 50th

• 83rd

• 86th

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The area under the standard Normal curve corresponding to –0.3 < Z < 1.6 is

• 0.327

• 0.471

• 0.563

• 0.954

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The wait time at your local McDonald's varies according to a normal distribution, with a mean of 7 minutes and standard deviation of 1.35 minutes. Approximately what proportion of their wait times are over 9 minutes?

• 0.033

• 0.069

• 0.189

• 0.191

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Women’s heights are normally distributed with a mean of 63.7 inches and a standard deviation of 2.9 inches. The United States Air Force will reject female pilot applicants that are in the top 10% and bottom 5% of all women heights (due to cockpit restrictions). Which of the following interval of heights will the USAF accept?

• 60 inches to 69.3 inches

• 58 inches to 69.3 inches

• 58.9 inches to 67.4 inches

• 60 inches to 67.4 inches

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Mrs. G's newborn baby girl sleeps for approximately 20.1 hours per day. Newborn sleep schedules are normally distributed with a standard deviation of 0.8 hours. If you know Mrs. G's daughter is at the 67th percentile for sleep, what is the mean sleep time of all newborn baby girls?

• 19.75 hours

• 19.98 hours

• 20.45 hours

• 18.45 hours

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Your favorite bag of candy says that it should have 8oz of the candy in the bag. You weigh the contents and find that you have 7.8oz. You log onto the candy's website to write a strongly worded email, and see that they have a disclaimer that the weights of the bags will vary according to a Normal Distribution with a weight of 8oz and a standard deviation of 0.25oz. Which of the following is an appropriate conclusion based on this information?

• 7.8oz is still a reasonable weight of your candy bag, since it falls 0.8oz below the mean.

• 7.8oz is still a reasonable weight of your candy bag, since it falls 0.8 standard deviations below the mean.

• 7.8 is not a reasonable weight of your candy bag, since it falls below the mean.

• 7.8 is not a reasonable weight of your candy bag, since it falls above the mean.

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