Question 1

What does the total area under any probability density function (such as the standard normal curve) represent?

Accepted Answer

The total probability, which is 1

Question 2

If the area to the left of $$z = 1.23 is$$ $$0.8907$$, what is the area to the right of $$z = 1.23$$?

Accepted Answer

$$1 - 0.8907 = 0.1093$$

Question 3

Which of the following best describes what a standard normal table provides?

Accepted Answer

The area to the left of a given z-score

Question 4

Suppose you want to find the probability that a value is between $$z = 1$$ and $$z = 2 on $$the standard normal curve. Which calculation is correct?

Accepted Answer

$$P = 0.9772 - 0.8413$$

Question 5

If the area to the left of $$z = -2 is$$ $$0.0228$$, what does this value represent?

Accepted Answer

The probability that a value is less than $$z = -2$$

Question 6

Which formula would you use to find the area to the right of a given z-score $$z_0$$?

Accepted Answer

$$1 - P(Z \u003c z_0$)$$

Question 7

A student uses a calculator to find the area between $$z = -1$$ and $$z = 2$$ using the normalcdf function. Which input is correct?

Accepted Answer

normalcdf(-1, 2)

Question 8

Why might answers differ slightly when using the standard normal table versus a calculator for finding areas under the curve?

Accepted Answer

The table values are rounded, while the calculator uses more decimal places

Question 9

If you want to use your calculator to find the area to the left of $$z = 2$$, which of the following is the best input?

Accepted Answer

normalcdf(-999, 2)

Question 10

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

Accepted Answer

The area to the left of $$z = 0 is$$ $$0.5000$$

Question 11

A hospital wants to know the probability that a patient’s test result is more than 3 standard deviations above the mean. Which calculation gives this probability?

Accepted Answer

$$1 - 0.9987$$

Question 12

If you want to find the area between $$z = -1$$ and $$z = 1$$, and the area to the left of $$z = 1 is$$ $$0.8413$$ and to the left of $$z = -1 is$$ $$0.1587$$, what is the area between?

Accepted Answer

$$0.8413 - 0.1587 = 0.6826$$

Question 13

Which of the following is the correct interpretation of the shaded area under the standard normal curve between $$z = 1$$ and $$z = 2$$?

Accepted Answer

The probability that $$Z is $$between 1 and 2

Question 14

Which of the following is NOT a correct way to find the area to the right of $$z = 1.23$$?

Accepted Answer

$$P(Z \u003c 1.23)$$

Question 15

A researcher wants to find the probability that a value falls below $$z = -2.5. $$Which value should they use from the standard normal table?

Accepted Answer

The area to the left of $$z = -2.5$$

Areas Under the Standard Normal Curve and Their Applications

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