Question 1

Which of the following best describes the purpose of the standard normal distribution table?

Accepted Answer

To find the probability that a value falls within a certain range in a normal distribution.

Question 2

Suppose the heights of adult men are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the $$z-$$score for a man who is 76 inches tall?

Accepted Answer

$$z = \frac{76 - 70}{3} = 2$$

Question 3

If $$z = 1.2$$, what is the area to the left of $$z$$ under the standard normal curve?

Accepted Answer

0.8840

Question 4

A hospital wants to know the probability that a randomly selected patient’s blood pressure is more than 2 standard deviations above the mean. What is this probability?

Accepted Answer

$$P(z \u003e 2) = 1 - 0.9772 = 0.0228$$

Question 5

Which $$z-$$score corresponds to the 95th percentile in the standard normal distribution?

Accepted Answer

$$z = 1.65$$

Question 6

A standardized test has scores that are normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that a randomly selected student scores less than 350?

Accepted Answer

$$z = \frac{350-500}{100} = -1.5$$, \ P(z \u003c -1.5) = 0.0668$

Question 7

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

Accepted Answer

$$z = 1.0$$

Question 8

A company finds that the time to assemble a product is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. What proportion of products take between 25 and 35 minutes to assemble?

Accepted Answer

$$z_1$$ = \frac{25-30}{5} = -1$$, z_2$ = \frac{35-30}{5} = 1$$, $$P(-1 \u003c z \u003c 1) = 0.6826$$

Question 9

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

Accepted Answer

The area to the left of $$z = 0 is 0.25.$$

Question 10

A researcher wants to find the probability that a randomly selected value from a standard normal distribution is less than $$z = -1.2. $$What is this probability?

Accepted Answer

0.1151

Question 11

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

Accepted Answer

$$a = 1.96$$

Question 12

A machine fills bottles with a mean of 500 ml and a standard deviation of 10 ml. What is the probability that a bottle contains more than 520 ml?

Accepted Answer

$$z = \frac{520-500}{10} = 2$$, $$P(z \u003e 2) = 0.0228$$

Question 13

Which of the following is the correct formula for converting a raw score $$x to a$$ $$z-$$score?

Accepted Answer

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

Question 14

If the area to the right of $$z is 0.05$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.645$$

Question 15

A university claims that the average IQ of its students is 110 with a standard deviation of 15. What percentage of students have an IQ between 95 and 125?

Accepted Answer

$$z_1$$ = \frac{95-110}{15} = -1$$, z_2$ = \frac{125-110}{15} = 1$$, $$P(-1 \u003c z \u003c 1) = 0.6826$$

Question 16

If $$z = -2.0$$, what is the area to the left of $$z$$ under the standard normal curve?

Accepted Answer

0.0228

Question 17

A pharmaceutical company finds that the weights of its pills are normally distributed with a mean of 500 mg and a standard deviation of 5 mg. What is the probability that a randomly selected pill weighs less than 490 mg?

Accepted Answer

$$z = \frac{490-500}{5} = -2$$, $$P(z \u003c -2) = 0.0228$$

Question 18

If $$z = 0.5$$, what is the area to the right of $$z$$ under the standard normal curve?

Accepted Answer

$$1 - 0.6915 = 0.3085$$

Question 19

A psychologist wants to know the probability that a randomly selected person scores between $$z = -1.96$$ and $$z = 1.96 on a $$standardized test. What is this probability?

Accepted Answer

$$P(-1.96 \u003c z \u003c 1.96) = 0.9500$$

Using the Standard Normal Distribution Table in Introductory Statistics

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