**MATH 215**

**TEST 2 - EXTRA CREDIT REVIEW ASSIGNMENT**

**CHAPTER 6 THE NORMAL DISTRIBUTION**

Indicate whether each of the following statements is TRUE or FALSE. If FALSE, change or add a word(s) or phrase(s) to the statement to make it TRUE.

T **F** 1. A probability density curve represents the probability distribution of a ** continuous** variable.

T F 2. The total area under the curve of ANY probability density curve is equal to 1.

T F 3. The mean, median, and mode of normally distributed data are all the same.

T F 4. The mean of the standard normal distribution is 1.

T F 5. The standard deviation of the standard normal distribution is 0.

T F 6. The Empirical Rule applies only to approximately normal, or bell-shaped distributions.

T F 7. The Empirical Rule states that approximately 65% of the data lies within one standard deviation of the mean, 98% of the data is within two standard deviations, and almost all data is within three standard deviations.

T F 8. If you needed to calculate the z-score that corresponded to the 64^{th} percentile of the standard normal distribution, the calculator command you would use would be **normalcdf**.

T F 9. The notation refers to the z-score with an area of to the left.

T F 10. When finding a value of , can be any value from to .

T F 11. The correct calculator command to calculate the percentage of data in the standard normal distribution that is less than z = - 0.56 would be **normalcdf(-0.56, 1E99, 1, 0)**.

T F 12. In this course, we never use **normal pdf**.

T F 13. **Normalcdf **is the calculator command we use to calculate probabilities and areas for any type of normal distribution, and that command requires four inputs, which are in order: the mean (), standard deviation (), the left bound, and the right bound of your data range.

T F 14. **Invnorm** is the calculator command we use to calculate z-scores when given an area, probability, or percentile for a normal distribution, and that command requires three inputs, which are in order: the mean (), standard deviation (), and the area to the right.

T F 15. = 1.96 (rounded to two decimal places).

T F 16. Suppose scores on the next statistics exam are normally distributed with an average of 74 and a standard deviation of 9. Then, we should expect approximately 10% of students to earn a score of 92 or better.

T F 17. The sampling distribution of means is made up of multiple values of , one for each random sample taken.

T F 18. The Central Limit Theorem (for means) states that if is the mean of a large () simple random sample from a population with mean and standard deviation , then has an approximately normal distribution, with mean and standard deviation

.

T F 19. The Central Limit Theorem (for proportions) states that if is the sample proportion with a sample size of and population proportion , and if and , then the distribution of is approximately normal, with mean and standard deviation .

20. Suppose you conducted exit polling at your voting location for a recent election, and 52% of the 200 randomly selected voters you spoke with said they voted for candidate A. Later that evening the news reports that at your location, candidate A only received 47% of the vote. Should you be concerned about possible voting fraud? If the news report is correct, what is the probability that 52% (or more) of your sampled voters would have voted for candidate A?

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