STAT Chapter 5

the total relative frequency must equal

1 (or 100%)

the standard score is positive for data values _______ the mean

above

The Central Limit Theorem applies to variables with

any distribution (not necessarily a normal distribution)

the normal distribution is spread out in a way that makes it look like the shape of a

bell

what is the formula for calculating standard score/Z-score?

data value-mean/standard deviation

a larger standard deviation looks

flatter

The Central Limit Theorem applies for suitably

large sample sizes

the standard deviation of the distribution of means approaches (standard deviation of the population/square root of a variable with any distribution) for

large sample sizes

the peak of a normal distribution corresponds to the

mean, median, and mode of the distribution

a distribution that has a larger standard deviation means that there is

more variation

The distribution of means will be approximately a

normal distribution

the distribution of means will be an approximately ____ ________ for large sample sizes

normal distribution

The mean of the distribution of means approaches the

population mean

the mean of the distribution of means approaches the _________ ____ for large sample sizes

population mean

the percentage of the total area in any region under the normal curve tells us the

relative frequency of data values

the area that lies under a normal distribution curve corresponding to a range of values on the horizontal axis is the

relative frequency of those values

number of standard deviations a data value lies above or below the mean

standard score (or Z-score)

values that lie more than 2 standard deviations away from the mean

unusual values

the normal distribution has _ peak

1

among all values, 5% lie more than _ standard deviations from the mean

2

95% of all values from a normal distribution lie within

2 standard deviations from the mean

Choose the correct definition of a standard score below. A. A standard score is the number of standard deviations a data value lies above or below the mean. B. A standard score is a data value equal to the mean. C. A standard score is the distance between a data value and the nearest outlier. D. A standard score is a data value that lies within one standard deviation of the mean.

A

Determine whether the following data set is likely to be normally distributed. Explain the reasoning. The pulse rates of randomly selected females. Choose the correct answer below. A. Normally distributed. The pulse rates vary above and below the mean by similar amounts. The distribution has one peak and is symmetric. Pulse rates result from a combination of many factors. B. Not normally distributed. Most people will have rates above the average causing a peak in the distribution at the right. nothing nothing C. Normally distributed because any large data set yields normally distributed values. D. Not normally distributed. Adult pulse rates will be about the same for each person comma causing a flat distribution curve characteristic of a uniform distribution.

A

Why is the standard deviation in part a different from the standard deviation in part​ b? Choose the correct answer below. A. With smaller sample sizes​ (as in part​ a), the means tend to be further​ apart, so they have more​ variation, which results in a smaller standard deviation. B. With smaller sample sizes​ (as in part​ a), the means tend to be closer​ together, so they have less​ variation, which results in a smaller standard deviation. C. With larger sample sizes​ (as in part​ b), the means tend to be closer​ together, so they have less​ variation, which results in a smaller standard deviation. D. With larger sample sizes​ (as in part​ b), the means tend to be further​ apart, so they have more​ variation, which results in a bigger standard deviation.

C

Decide whether the following statement makes sense or does not make sense. Explain your reasoning. My professor graded the final score on a​ curve, and she gave a grade of A to anyone who had a standard score of 2 or more. Choose the correct answer below. A. This makes sense because now the majority of the class is receiving an A on the​ test, which is very fair. B. This does not make sense because a standard score of 2 or more corresponds to roughly the 97th percentile. This means the lowest test scores are getting curved up to be the highest test scores. C. This does not make sense because it is rare for test scores to follow the normal distribution. D. This makes sense because a standard score of 2 or more corresponds to roughly the 97th percentile. Though this curve is stingy on giving out​ A's to​ students, it is still giving the top students the highest grade.

D

What does the area under the normal distribution curve​ represent? What is the total area under the normal distribution​ curve? A. The area that lies under the normal distribution curve corresponding to a range of values on the horizontal axis is the cumulative frequency of those values. Because the total cumulative frequency for all values must be equal to the total​ frequency, the total area under the normal distribution curve must equal the total frequency. B. The area that lies under the normal distribution curve has no​ meaning, but the area under the normal distribution curve above a single value on the horizontal axis represents the cumulative frequency of that value. Because the area below the normal distribution curve in between two values on the horizontal axis has no meaningful​ interpretation, the total area under the curve also has no meaningful interpretation. C. The area that lies under the normal distribution curve has no​ meaning, but the area under the normal distribution curve above a single value on the horizontal axis represents the relative frequency of that value. Because the area below the normal distribution curve in between two values on the horizontal axis has no meaningful​ interpretation, the total area under the curve also has no meaningful interpretation. D. The area that lies under the normal distribution curve corresponding to a range of values on the horizontal axis is the total relative frequency of those values. Because the total relative frequency for all values must be 1​ (100%), the total area under the normal distribution curve must equal 1​ (100%).

D

When referring to a​ "normal" distribution, does the word normal have the same meaning as it does in ordinary​ usage? Explain. A. The word normal does not have special meaning in statistics. It refers to a distribution which reflects an average and expected underlying dataset with few to no outliers. B. The word normal has a special meaning in statistics. It refers to a specific category of distributions that are symmetric and flat. Normal distributions have rectangular areas below their distribution curves. C. The word normal does not have special meaning in statistics. It refers to a distribution which reflects a dataset where all the members of the dataset are close to the average of the dataset. D. The word normal has a special meaning in statistics. It refers to a specific category of distributions that are symmetric and​ bell-shaped with a single peak. The peak corresponds to the​ mean, median, and mode of such a distribution.

D