Question 1

Suppose the cholesterol levels in a population are normally distributed with a mean of 200 mg/dL and a standard deviation of 20 mg/dL. What is the probability that a randomly selected individual has a cholesterol level less than 220 mg/dL? (Use the standard normal distribution and $$z-$$table.)

Accepted Answer

$$P(Z \u003c 1) = 0.8413$$

Question 2

A hospital wants to know the probability that a patient’s body temperature is above 99°F, given that body temperatures are normally distributed with a mean of 98.6°F and a standard deviation of 0.4°F. What is the probability that a randomly selected patient has a temperature above 99°F?

Accepted Answer

$$P(Z \u003e 1) = 1 - 0.8413 = 0.1587$$

Question 3

Which of the following best describes the value given in a standard $$z-$$table?

Accepted Answer

The cumulative probability to the left of a given $$z-$$score.

Question 4

If $$P(Z \u003c z) = 0.9332$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.5$$

Question 5

A researcher wants to find the probability that a randomly selected value from a standard normal distribution falls between $$z = -0.64$$ and $$z = 2.77. $$Which calculation is correct?

Accepted Answer

$$P(-0.64 \u003c Z \u003c 2.77) = P(Z \u003c 2.77) - P(Z \u003c -0.64)$$

Question 6

If the area to the left of a $$z-$$score is 0.6433, what is the $$z-$$score?

Accepted Answer

$$z = 0.36$$

Question 7

A pharmaceutical company wants to know the probability that a randomly selected pill weighs less than 1.21 standard deviations above the mean. What is this probability?

Accepted Answer

$$P(Z \u003c 1.21) = 0.8869$$

Question 8

Which formula would you use to find the probability to the right of a $$z-$$score using the $$z-$$table?

Accepted Answer

$$P(Z \u003e z) = 1 - P(Z \u003c z)$$

Question 9

A student scores 0.44 standard deviations below the mean on a test. What is the probability that a randomly selected student scores less than this student?

Accepted Answer

$$P(Z \u003c -0.44) = 0.3300$$

Question 10

If $$P(Z \u003e z) = 0.0668$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.5$$

Question 11

A biologist measures the heights of a species of plant and finds they are normally distributed with mean 50 cm and standard deviation 5 cm. What is the probability that a randomly selected plant is taller than 60 cm?

Accepted Answer

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

Question 12

Which of the following steps is correct when finding the probability between two $$z-$$scores using the $$z-$$table?

Accepted Answer

Subtract the area to the left of the smaller $$z-$$score from the area to the left of the larger $$z-$$score.

Question 13

A psychologist wants to find the $$z-$$score such that 95% of the population scores below it. What is the $$z-$$score?

Accepted Answer

$$z = 1.645$$

Question 14

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

Accepted Answer

$$z = 0$$

Question 15

A company wants to know the probability that a randomly selected employee’s score is between $$z = -1$$ and $$z = 1. $$What is this probability?

Accepted Answer

$$P(-1 \u003c Z \u003c 1) = P(Z \u003c 1) - P(Z \u003c -1) = 0.8413 - 0.1587 = 0.6826$$

Question 16

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

Accepted Answer

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

Question 17

A medical test result is considered positive if it is above the 90th percentile. What is the $$z-$$score corresponding to the 90th percentile?

Accepted Answer

$$z = 1.28$$

Question 18

If $$P(Z \u003c z) = 0.5$$, what does this tell you about the $$z-$$score and the distribution?

Accepted Answer

The $$z-$$score is at the mean of the standard normal distribution.

Standard Normal Distribution and Using the z-Table

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