Question 1

A student earns 85 on a statistics test. The mean of the test is 76 with a standard deviation of 3. What is the z-score for the student's test score?

Accepted Answer

$$z = \frac{85 - 76}{3}$$

Question 2

If a test score has a z-score of $$1.5$$, what does this indicate about the score's position relative to the mean?

Accepted Answer

It is $$1.5$$ standard deviations above the mean.

Question 3

Given a normal distribution with mean $$\mu = 20$$ months and standard deviation $$\sigma = 2$$ months, what is the z-score for a popcorn maker that lasts $$16$$ months?

Accepted Answer

$$z = \frac{16 - 20}{2}$$

Question 4

If $$P(z \u003c 1.23)$$, what does this probability represent on the standard normal curve?

Accepted Answer

The area to the left of $$z = 1.23$$

Question 5

A manufacturer wants to set a guarantee period so that no more than $$3\% of $$popcorn makers are replaced. If the lifetimes are normally distributed with mean $$20$$ months and standard deviation $$2$$ months, what z-score should be used to find the guarantee period?

Accepted Answer

$$z = -1.88$$

Question 6

If $$10\% of $$the area under the standard normal curve lies to the right of $$z$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.28$$

Question 7

What is the probability that a randomly selected value from a standard normal distribution is less than $$z = 0$$?

Accepted Answer

$$0.5$$

Question 8

If $$90.3\% of $$the area under the standard normal curve lies between $$-z$$ and $$z$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.68$$

Question 9

A hiker's pack weight is normally distributed with mean $$\mu = 40$$ lbs and $$\sigma = 10.4$$ lbs. What is the probability that a randomly selected pack weighs less than $$60$$ lbs?

Accepted Answer

Find $$z = \frac{60 - 40}{10.4}$$ and use the standard normal table.

Question 10

If the probability that a value is more than $$85$$ inches in a normal distribution with mean $$70$$ inches and standard deviation $$5$$ inches is required, what is the first step?

Accepted Answer

Calculate $$z = \frac{85 - 70}{5}$$

Question 11

Which of the following best describes the area under the standard normal curve?

Accepted Answer

The total area is $$1$$

Question 12

If $$P(z \u003e 2.00)$$, what does this probability represent?

Accepted Answer

The area to the right of $$z = 2.00$$

Precalculus Statistics Quiz: Normal Distribution and Z-Scores Study Guidance

Study Guide - Practice Questions

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