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 64th 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 normalpdf.

 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?