QUESTIONS
Question 1
Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Question 2
Annie averages 23 points per basketball game with a standard deviation of 4 points. Suppose Annie’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(23,4).
Suppose Annie scores 34 points in the game on Sunday. The z-score when x=34 is _1__ The mean is _2__.
This z-score tells you that x=34 is _3__ standard deviations to the right of the mean.
Question 3
Rosetta averages 148 points per bowling game with a standard deviation of 14 points. Suppose Rosetta’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14).
If necessary, round to three decimal places.
Suppose Rosetta scores 110 points in the game on Thursday. The z-score when x=110 is 1___ The mean is 2___
This z-score tells you that x=110 is 3___ standard deviations to the left of the mean.
Question 4
Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Question 5
Annie was told that her math test score was 3 standard deviations below the mean. If test scores were approximately normal with μ=99 and σ=4, what was Annie’s score? Do not include units in your answer. For example, if you found that the score was 99 points, you would enter 99.
Question 6
Alice was told that her reading test score was 2 standard deviations below the mean. If test scores were approximately normal with μ=84 and σ=8, what was Alice’s score?
Question 7
Isabella averages 152 points per bowling game with a standard deviation of 14.5 points. Suppose Isabella’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(152,14.5).
If necessary, round to three decimal places.
Suppose Isabella scores 187 points in the game on Sunday. The z-score when x=187 is 1___ The mean is 2___
This z-score tells you that x = 187 is 3___ standard deviations to the right of the mean.
Question 8
Suppose X∼N(10,0.5), and x=11.5. Find and interpret the z-score of the standardized normal random variable.
The z-score when x=11.5 is 1___. The mean is 2___.
This z-score tells you that x=11.5 is 3___ standard deviations to the right of the mean.
Question 9
Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Question 10
Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Question 11
The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the largest mean.
Question 12
The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the largest mean.
Question 13
Jamie was told that her reading test score was 1 standard deviation above the mean. If test scores were approximately normal with μ=97 and σ=10, what was Jamie’s score?
Question 14
Marc’s points per game of bowling are normally distributed with a standard deviation of 13 points. If Marc scores 231 points, and the z-score of this value is 4, then what is his mean points in a game? Do not include the units in your answer. For example, if you found that the mean is 150 points, you would enter 150.
ANSWERS:
Question 1
Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Answer:
B has the larger mean.
A has the larger standard deviation.
Question 2
Annie averages 23 points per basketball game with a standard deviation of 4 points. Suppose Annie’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(23,4).
Suppose Annie scores 34 points in the game on Sunday. The z-score when x=34 is _1__ The mean is _2__.
This z-score tells you that x=34 is _3__ standard deviations to the right of the mean.
Answer:
1 = 2.75
2 =23
3 =2.75
Question 3
Rosetta averages 148 points per bowling game with a standard deviation of 14 points. Suppose Rosetta’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14).
If necessary, round to three decimal places.
Suppose Rosetta scores 110 points in the game on Thursday. The z-score when x=110 is 1___ The mean is 2___
This z-score tells you that x=110 is 3___ standard deviations to the left of the mean.
Answer:
1 = -2.714
2 = 148
3 = 2.714
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