Question 1

Which of the following best describes a continuous probability distribution?

Accepted Answer

It represents the probability of a random variable falling within a range of values.

Question 2

The total area under the curve of a normal distribution is:

Accepted Answer

$$1$$

Question 3

If the mean of a normal distribution increases while the standard deviation remains the same, what happens to the curve?

Accepted Answer

The peak of the curve shifts to the right on the number line.

Question 4

Given a normal distribution with mean $$\mu = 10.25$$ and standard deviation $$\sigma = 0.50$$, what is the $$z-$$score for $$x = 11$$?

Accepted Answer

$$z = \frac{11 - 10.25}{0.50} = 1.5$$

Question 5

Which statement about standard deviation in a normal distribution is correct?

Accepted Answer

Increasing the standard deviation makes the curve wider and less peaked.

Question 6

For a standard normal distribution, what is the probability that $$z \u003c -1$$?

Accepted Answer

$$0.1587$$

Question 7

A fast food chain dispenses drinks with a mean of $$10.25 oz $$and a standard deviation of $$0.50 oz. $$What is the probability of getting a drink with less than $$10 oz$$?

Accepted Answer

$$P(z \u003c -0.5) = 0.3085$$

Question 8

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

Accepted Answer

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

Question 9

If $$P(z \u003c a) = 0.60$$, what is the closest $$z-$$score for $$a$$?

Accepted Answer

$$z = 0.25$$

Question 10

In a normal distribution, what is the probability that $$z \u003e 1.37$$?

Accepted Answer

$$0.0606$$

Question 11

For a normal distribution, which of the following statements is true about negative $$z-$$scores?

Accepted Answer

They represent values below the mean.

Question 12

A graduate exam has scores normally distributed with mean $$\mu = 62$$ and standard deviation $$\sigma = 6.3. $$What proportion of students scored greater than $$53$$?

Accepted Answer

$$0.9236$$

Question 13

If you want to find the $$x-$$value such that $$90\% of $$exam scores are above it in a normal distribution with $$\mu = 62$$ and $$\sigma = 6.3$$, what is the $$z-$$score you should use?

Accepted Answer

$$z = -1.28$$

Question 14

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

Accepted Answer

It is skewed to the right.

Question 15

If $$P(z  1.37)$$?

Accepted Answer

$$0.0606$$

Question 16

A normal distribution has $$\mu = 10.25$$ and $$\sigma = 0.50. $$What $$x-$$values contain the middle $$75\% of $$the data symmetric around the mean?

Accepted Answer

$$9.675$$ and $$10.825$$

Question 17

Which of the following best explains how probabilities are found for intervals in a normal distribution?

Accepted Answer

By calculating the area under the curve for that interval.

Question 18

If $$P(z \u003c -0.32) = 0.3745$$ and $$P(z \u003c 1.37) = 0.9144$$, what is $$P(-0.32 \u003c z \u003c 1.37)$$?

Accepted Answer

$$0.5399$$

Question 19

Which of the following is true about the area under the normal curve?

Accepted Answer

The area to the right of the mean is always $$0.50.$$

The Normal Distribution: Properties, Z-Scores, and Probability Calculations

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