Question 1

Which of the following best describes the standard normal distribution?

Accepted Answer

A distribution with mean $$\mu = 0$$ and standard deviation $$\sigma = 1$$

Question 2

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

Accepted Answer

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

Question 3

What is the probability that a randomly selected value from a standard normal distribution is less than $$z = 0.75$$?

Accepted Answer

$$0.7734$$

Question 4

A medical test result is $$2$$ standard deviations above the mean. What is the probability that a randomly selected result is less than this value?

Accepted Answer

$$0.9772$$

Question 5

Which formula is used to convert a raw score $$x to a$$ $$z-$$score in a normal distribution?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 6

If the area to the left of $$z is$$ $$0.8413$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.0$$

Question 7

A company finds that the time to assemble a product is normally distributed with mean $$\mu = 30$$ minutes and standard deviation $$\sigma = 5$$ minutes. What is the $$z-$$score for an assembly time of $$40$$ minutes?

Accepted Answer

$$z = 2.0$$

Question 8

What is the probability that a value from a standard normal distribution is greater than $$z = 1.28$$?

Accepted Answer

$$0.1003$$

Question 9

If $$P(Z \u003c z) = 0.0250$$, what is the value of $$z$$?

Accepted Answer

$$z = -1.96$$

Question 10

A student scores $$85 on a $$test with mean $$80$$ and standard deviation $$4. $$What is the student's $$z-$$score?

Accepted Answer

$$z = 1.25$$

Question 11

What is the area between $$z = -1.0$$ and $$z = 1.0 in $$the standard normal distribution?

Accepted Answer

$$0.6826$$

Question 12

If the area to the right of $$z is$$ $$0.1587$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.0$$

Question 13

A hospital records the weights of newborns as normally distributed with mean $$\mu = 3.5 kg $$and $$\sigma = 0.5 kg. $$What is the probability that a newborn weighs less than $$2.5 kg$$?

Accepted Answer

$$0.0228$$

Question 14

Which of the following statements is TRUE about the standard normal distribution?

Accepted Answer

It is symmetric about $$z = 0.$$

Question 15

If $$z = -2.33$$, what is the area to the left of $$z$$?

Accepted Answer

$$0.0099$$

Question 16

A researcher wants to find the probability that a value is between $$z = 0$$ and $$z = 1.5. $$What is the correct probability?

Accepted Answer

$$0.4332$$

Question 17

If $$P(Z \u003c z) = 0.9750$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.96$$

Question 18

A value is at the $$90th $$percentile of the standard normal distribution. What is its $$z-$$score?

Accepted Answer

$$z = 1.28$$

Question 19

Which of the following is NOT a property of the standard normal distribution?

Accepted Answer

The total area under the curve is $$2.$$

Question 20

A psychologist finds that IQ scores are normally distributed with mean $$100$$ and standard deviation $$15. $$What is the probability that a randomly selected person has an IQ less than $$85$$?

Accepted Answer

$$0.1587$$

Using the Standard Normal Distribution Table in Statistics

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