Question 1

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

Accepted Answer

The normal curve is skewed to the right.

Question 2

Suppose the heights of adult men are normally distributed with mean $$\mu = 70$$ inches and standard deviation $$\sigma = 3$$ inches. Which of the following statements is TRUE about the normal curve for this distribution?

Accepted Answer

The inflection points occur at $$x = 67$$ and $$x = 73.$$

Question 3

A standard normal distribution has which of the following characteristics?

Accepted Answer

Mean $$\mu = 0$$, standard deviation $$\sigma = 1$$

Question 4

Given a standard normal distribution, what is the cumulative area to the left of $$z = 0$$?

Accepted Answer

$$0.5$$

Question 5

If the cumulative probability to the left of $$z = -2.16 is$$ $$0.0154$$, what is the probability that a randomly selected value from the standard normal distribution is greater than $$z = -2.16$$?

Accepted Answer

$$0.9846$$

Question 6

Which normal curve has the largest standard deviation?

Accepted Answer

The curve that is the most spread out.

Question 7

A hospital records the weights of newborns, which are normally distributed with mean $$\mu = 3.5 kg $$and standard deviation $$\sigma = 0.5 kg. $$What is the $$z-$$score for a newborn weighing $$4.0 kg$$?

Accepted Answer

$$z = 1.0$$

Question 8

Find the area under the standard normal curve between $$z = -2.17$$ and $$z = -1.35$$ given that $$P(Z \u003c -2.17) = 0.0150$$ and $$P(Z \u003c -1.35) = 0.0885.$$

Accepted Answer

$$0.0735$$

Question 9

Which of the following best describes the inflection points of a normal curve?

Accepted Answer

Where the curve changes from curving upward to curving downward.

Question 10

A pharmaceutical company finds that the time to dissolve for a new tablet is normally distributed with mean $$\mu = 20$$ minutes and standard deviation $$\sigma = 2$$ minutes. What is the probability that a randomly selected tablet dissolves in less than $$22.5$$ minutes? (Use the standard normal table: $$z = 1.25$$ corresponds to $$P(Z \u003c 1.25) = 0.8944.)$$

Accepted Answer

$$0.8944$$

Question 11

If the cumulative area for $$z = 1.23 is$$ $$0.8907$$, what does this value represent?

Accepted Answer

The probability that $$z is $$less than $$1.23.$$

Question 12

A researcher wants to find the probability that a standard normal variable falls to the left of $$z = -1.5. $$Which of the following steps is correct?

Accepted Answer

Look up $$z = -1.5 in $$the standard normal table.

Question 13

Which of the following statements about the area under the standard normal curve is TRUE?

Accepted Answer

The area to the left of $$z = -3.49 is $$close to $$0.$$

Question 14

A normal distribution has mean $$\mu = 50$$ and standard deviation $$\sigma = 5. $$Which $$x-$$value corresponds to $$z = 2$$?

Accepted Answer

$$x = 60$$

Question 15

If the area to the left of $$z = 1.15 is$$ $$0.8749$$, what is the area to the right of $$z = 1.15$$?

Accepted Answer

$$0.1251$$

Question 16

Which of the following best explains why the total area under any normal curve is always 1?

Accepted Answer

Because it represents the total probability for all possible outcomes.

Question 17

A psychologist is studying reaction times, which are normally distributed with mean $$\mu = 250 ms $$and standard deviation $$\sigma = 30 ms. $$What is the probability that a randomly selected reaction time is between $$220 ms $$and $$280 ms$$? (Use $$z = -1$$ and $$z = 1$$, with $$P(Z \u003c 1) = 0.8413$$ and $$P(Z \u003c -1) = 0.1587.)$$

Accepted Answer

$$0.6826$$

Normal Probability Distributions and Areas Under the Curve

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