STATS 1.10 Normal Distribution

The distribution of the number of transactions per day at a certain automated teller machine (ATM) is approximately normal with a mean of 80 transactions and a standard deviation of 10 transactions. Which of the following represents the parameters of the distribution?

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• 
• 
• 
• 

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CCSS.HSS.ID.A.4

Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the distribution?

• 
  80 years

• 
  115 years

• 
  120 years

• 
  125 years

• 
  130 years

At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?

• 0.17

• 0.25

• 0.36

• 0.83

• 0.95

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CCSS.HSS.ID.A.4

At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the chemistry final and 84 on the calculus final. Relative to the students in each respective class, in which subject did this student do better?

• The student did better in chemistry.

• The student did better in calculus.

• The student did equally well in each course

• There is no basis for comparison, since the subjects are different from each other .

• There is not enough information for comparison, because the number of students is not known.

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CCSS.HSS.ID.A.4

Some descriptive statistics for a set of test scores are shown above. For this test, a certain student has a standardized score of z = -1.2. What score did this student receive on the test?

• 266.28

• 779.42

• 1008.02

• 1083.38

• 1311.98

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CCSS.HSS.ID.A.4

A sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies?

• 15.1

• 15.3

• 16.1

• 16.5

• 16.7

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The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams (mg). A randomly selected 8-ounce can containing 35 mg of caffeine is 1.2 standard deviations above the mean. Approximately what percent of 8-ounce cans of the cola have a caffeine content greater than 35 mg?

• 1%

• 8%

• 12%

• 16%

• 99%

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CCSS.HSS.ID.A.4

For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season?

• 250 yards

• 300 yards

• 350 yards

• 400 yards

• 450 yards

The weight of adult male grizzly bears living in the continental US is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds?

• 276 pounds

• 324 pounds

• 330 pounds

• 342 pounds

• 533 pounds

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CCSS.HSS.ID.A.4

Height, in meters, is measured for each person in a sample. After the data are collected, all the height measurements are converted from meters to centimeters by multiplying each measurement by 100. Which of the following statistics will remain the same for both units of measure?

• The mean of the height measurement

• The median of the height measurements

• The standard deviation of the height measurements

• The maximum of the height measurements

• The z-scores of the height measurements