Q: Which of the following is the correct input to find the area to the right of $$z = 1.93$$ using a calculator?

$$\text{normalcdf}(1.93, 10$$^{99}$$, 0, 1)$$

Question 1

Which of the following best describes the area shaded in the first image (with $$z = -0.78$$)?

Accepted Answer

The area to the left of $$z = -0.78$$ under the standard normal curve.

Question 2

What is the probability represented by the shaded region in the first image (to the left of $$z = -0.78$$)?

Accepted Answer

$$0.2177$$

Question 3

In the second image, what does the shaded region represent?

Accepted Answer

The area to the right of $$z = -2.46$$ under the standard normal curve.

Question 4

Calculate the percentage of z-scores above $$z = -2.46 in a $$standard normal distribution.

Accepted Answer

$$99.31\%$$

Question 5

Which calculator function would you use to find the area between two z-scores in a standard normal distribution?

Accepted Answer

$$	ext{normalcdf}$$

Question 6

If you want to find the z-score that corresponds to the 40th percentile, which function and input would you use?

Accepted Answer

$$	ext{invNorm}(0.40, 0, 1)$$

Question 7

What is the z-score for the 40th percentile in a standard normal distribution?

Accepted Answer

$$-0.25$$

Question 8

Which z-score marks the lowest value in the top $$2.5\% of a $$standard normal distribution?

Accepted Answer

$$1.96$$

Question 9

Find the probability that a z-score is between $$z = 1.24$$ and $$z = 2.09 in a $$standard normal distribution.

Accepted Answer

$$0.0892$$

Question 10

Which of the following is the correct input to find the area to the right of $$z = 1.93$$ using a calculator?

Accepted Answer

$$	ext{normalcdf}(1.93, 10$$^{99}$$, 0, 1)$$

Question 11

If you want to find the z-scores that cut off the lowest $$15\%$$ and the highest $$20\% of a $$standard normal distribution, which values would you use?

Accepted Answer

$$z = -1.04$$ and $$z = 0.84$$

Question 12

A medical test result is considered 'extreme' if it falls in the top $$2.5\% of $$the standard normal distribution. What is the minimum z-score for an extreme result?

Accepted Answer

$$1.96$$

Question 13

Which of the following best describes the use of $$	ext{invNorm} on a $$calculator?

Accepted Answer

It finds the z-score corresponding to a given cumulative probability.

Question 14

If $$P(z \u003c a) = 0.15 in a $$standard normal distribution, what is the value of $$a$$?

Accepted Answer

$$-1.04$$

Question 15

A researcher wants to know the probability that a randomly selected value from a standard normal distribution is greater than $$z = 1.93. $$What is this probability?

Accepted Answer

$$0.0268$$

The Standard Normal Distribution: Calculating Areas and Percentiles

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