Chapter 6: The Normal Distribution and The Central Limit Theorem
Chapter 6: The Normal Distribution and The Central Limit Theorem
Chapter 6 Practice
Section 6.1 Practice
A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words. [latex]X = \text{____________}[/latex].
Solution
ounces of water in a bottle
A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?
Solution
61
If [latex]X \sim N(1, 2)[/latex], [latex]\sigma = \text{_______}[/latex]
Solution
2
A company manufactures rubber balls. The mean diameter of a ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. [latex]X = \text{______________}[/latex].
Solution
diameter of a rubber ball
If [latex]X \sim N( -4, 1)[/latex], what is the median?
Solution
–4
If [latex]X \sim N(3, 5)[/latex], [latex]\sigma = \text{_______}[/latex]
Solution
5
If [latex]X \sim N(-2, 1)[/latex], [latex]\mu = \text{_______}[/latex]
Solution
–2
What does a z-score measure?
Solution
The number of standard deviations a value is from the mean.
What does standardizing a normal distribution do to the mean?
Solution
The mean becomes zero.
Is [latex]X \sim N(0, 1)[/latex] a standardized normal distribution? Why or why not?
Solution
Yes because the mean is zero, and the standard deviation is one.
What is the z-score of [latex]x = 12[/latex], if it is two standard deviations to the right of the mean?
Solution
[latex]z = 2[/latex]
What is the z-score of [latex]x = 9[/latex], if it is 1.5 standard deviations to the left of the mean?
Solution
[latex]z = –1.5[/latex]
What is the z-score of [latex]x = –2[/latex], if it is 2.78 standard deviations to the right of the mean?
Solution
[latex]z = 2.78[/latex]
What is the z-score of [latex]x = 7[/latex], if it is 0.133 standard deviations to the left of the mean?
Solution
[latex]z = –0.133[/latex]
Suppose [latex]X \sim N(2, 6)[/latex]. What value of x has a z-score of three?
Solution
[latex]x = 20[/latex]
Suppose [latex]X \sim N(8, 1)[/latex]. What value of x has a z-score of –2.25?
Solution
[latex]x = 5.75[/latex]
Suppose [latex]X \sim N(9, 5)[/latex]. What value of x has a z-score of –0.5?
Solution
[latex]x = 6.5[/latex]
Suppose [latex]X \sim N(2, 3)[/latex]. What value of x has a z-score of –0.67?
Solution
[latex]x = –0.01[/latex]
Suppose [latex]X \sim N(4, 2)[/latex]. What value of x is 1.5 standard deviations to the left of the mean?
Solution
[latex]x = 1[/latex]
Suppose [latex]X \sim N(4, 2)[/latex]. What value of x is two standard deviations to the right of the mean?
Solution
[latex]x = 8[/latex]
Suppose [latex]X \sim N(8, 9)[/latex]. What value of x is 0.67 standard deviations to the left of the mean?
Solution
[latex]x = 1.97[/latex]
Suppose [latex]X \sim N(-1, 2)[/latex]. What is the z-score of [latex]x = 2[/latex]?
Solution
[latex]z = 1.5[/latex]
Suppose [latex]X \sim N(12, 6)[/latex]. What is the z-score of [latex]x = 2[/latex]?
Solution
[latex]z = –1.67[/latex]
Suppose [latex]X \sim N(9, 3)[/latex]. What