Questions and Answers
If the candy company's belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights?
What is the probability that the running time of a randomly selected remote control car is between 75 minutes and 82.5 minutes?
The probability of running time of a randomly selected car of this type is between 75 minutes and 82.5 minutes.
What is the best estimate of the z-score of the third quartile for a non-symmetric distribution of test scores?
The z-score cannot be estimated from the information given.
Which expression represents the weight at the 75th percentile of the distribution for the weights shipped?
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What is the approximate mean sleep time for newborn babies if a sleep time of 15.9 hours is at the 10th percentile?
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What score did a student receive on the test if their standardized score is z = -1.2?
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Which of the following intervals will contain the greatest proportion of cartons of large eggs?
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Relative to the students in each respective class, in which subject did the student do better?
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What is the closest proportion of orders processed in less than 240 seconds?
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What is the closest proportion of field mice with a weight greater than 33 grams?
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What is the standard deviation of the number of rushing yards for running backs that season?
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Which statistics remain the same when height measurements are converted from meters to centimeters?
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What is the correct order from least to greatest for the values of r, s, and t?
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What percent of participants had finishing times greater than Shalise's for each puzzle?
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What percent of hours will be the number of purchases at the online store exceed 1400?
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What is the closest value to the distribution of salmon lengths if 10 percent are longer than 30 inches?
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What is the standardized score for the student after the conversion if it was z = 1.72 before conversion?
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What is the closest standard deviation of the times taken by the 100 mice to navigate through the maze?
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What percent of 8 ounce cans of cola have a caffeine content greater than 35 mg?
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What is the probability that a student arrives at college later than 9 a.m. if they leave home at 8:25 a.m.?
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What is the closest percentage of assembly times between 4 minutes and 5 minutes?
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At what percentile is Aliyaah's height and how does it compare to Jayne's?
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What is the best estimate of the percent of one bedroom apartments in the city with a monthly rent of at most $800?
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What is the closest percent of the runners who weigh between 114 pounds and 138 pounds?
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What is the closest estimate for the mean of the height distribution for a 3 year old boy if Duncan is at the 32nd percentile and Shane is at the 62nd percentile?
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What is Rachael's height if she is at the 99th percentile in height for adult women?
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What would be the weight of a female grizzly bear with the same standardized score as a male grizzly bear weighing 530 pounds?
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Study Notes
Weight Distribution of Candies
- Candies produced by a company are normally distributed with a mean weight of 720 mg.
- The interval of weights containing the largest proportion is 700 mg to 740 mg.
Remote Control Car Running Times
- Running times for a specific remote control car are normally distributed with a mean of 80 minutes and a standard deviation of 2.5 minutes.
- The probability of running time between 75 minutes and 82.5 minutes is represented by the shaded area in a related figure.
Test Scores Distribution
- A non-symmetric distribution of test scores does not provide enough information to estimate the z-score at the third quartile accurately.
Producer Supplier Box Weights
- The weight distribution of produce boxes is approximately normal with a mean of 36 pounds and a standard deviation of 4 pounds.
- The weight at the 75th percentile can be expressed as 0.67(4) + 36.
Newborn Baby Sleep Times
- A sleep duration of 15.9 hours per day is at the 10th percentile for newborns.
- Assuming normal distribution with a 0.5-hour standard deviation, the mean sleep time for newborns is approximately 16.5 hours.
Standardized Test Scores
- A student with a standardized z-score of -1.2 on a test corresponds to a score of about 779.42.
Egg Carton Weights
- The weight distribution of large egg cartons is approximately normal with a mean of 26 ounces.
- The interval of weights containing the greatest proportion is between 24 oz to 28 oz.
Relative Performance in Exams
- Chemistry final scores normally distributed with mean 75 and standard deviation 12, Calculus scores with mean 80 and standard deviation 8.
- A student scored 81 in chemistry and 84 in calculus, performing equally well relative to classmates.
Order Processing Times
- Cashier processing times at a coffee shop follow a normal distribution with mean 276 seconds and standard deviation 38 seconds.
- Proportion of orders processed in less than 240 seconds is approximately 17%.
Mouse Weight Distribution
- The weight of field mice is normally distributed, mean of 25 grams and standard deviation of 4 grams.
- The proportion of mice weighing more than 33 grams is approximately 2.3%.
College Football Rushing Yards
- The mean rushing yardage recorded is 790 yards.
- A running back scoring 1,637 yards is 2.42 standard deviations above the mean, indicating a standard deviation of about 350 yards.
Height Measurement Conversion
- Height measurements converted from meters to centimeters maintain the same z-scores.
Order of Z-Scores
- In a normally distributed dataset:
- r (z = -1.00), s (first quartile), t (20th percentile).
- Correct order from least to greatest: r, t, s.
Jigsaw Puzzle Completion Times
- Shalise's completion times for puzzles:
- Small puzzle finished in 75 minutes (16% of participants slower).
- Large puzzle finished in 140 minutes (84% of participants slower).
Online Store Purchases
- The distribution of purchases is normal with a mean of 1200 and standard deviation of 200.
- The proportion of hours with purchases exceeding 1400 is approximately 16%.
Salmon Length Distribution
- Salmon lengths are normally distributed with a standard deviation of 3.5 inches.
- If 10% of salmon are longer than 30 inches, the mean length is approximately 26 inches.
Standardized Scores After Conversion
- Converting time from seconds to minutes does not change the standardized score (z-score).
Maze Navigation Times
- The standard deviation of recorded times for mice navigating a maze is close to 10 seconds.
Caffeine Content of Cola
- Caffeine content is normally distributed with a mean of 33 mg.
- Approximately 12% of cans have a caffeine content greater than 35 mg.
Student Commuting Times
- Commuting time follows a normal distribution with mean 30 minutes and standard deviation 5 minutes.
- The probability of arriving later than 9 a.m., if leaving at 8:25 a.m., is about 16%.
Smartphone Assembly Times
- Assembly time for smartphones has a mean of 4.6 minutes and a standard deviation of 0.6 minutes.
- Approximately 59% of assembly times fall between 4 and 5 minutes.
Heights of Children
- Heights of 6-year-old girls are normally distributed with a mean of 46 inches, standard deviation 2.7 inches.
- Aliyaah's height is at the 83rd percentile and is shorter than her friend Jayne at the 93rd percentile.
Rental Prices of Apartments
- Monthly rent for one-bedroom apartments is normally distributed, mean $936, standard deviation $61.
- About 1.3% of apartments have a rent at or below $800.
Weights of Cross Country Runners
- The distribution of weights of female college runners has a mean of 122 pounds, standard deviation 8 pounds.
- Approximately 82% of runners weigh between 114 pounds and 138 pounds.
Height of Young Boys
- The height distribution for 3-year-old boys indicates Duncan at the 32nd percentile (32 inches) and Shane at the 62nd percentile (34 inches).
- The mean height of the distribution is estimated around 33.21 inches.
Adult Women's Heights
- Adult women have a normally distributed height with a mean of 65 inches.
- Rachael, at the 99th percentile, is approximately 70 inches tall.
Grizzly Bear Weights
- Male grizzly bears weigh, on average, 500 pounds (standard deviation 50 pounds), while females average 300 pounds (standard deviation 40 pounds).
- A female bear with the same standardized score as a 530-pound male would weigh approximately 324 pounds.
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Test your knowledge on AP Statistics concepts with these flashcards tailored for Review Test 2. This set includes questions on normal distributions and statistical intervals, essential for mastering the material. Perfect for last-minute revisions and reinforcing learning.
