AP Stats Unit 2

Which of the following are properties of all normal distributions?

• Mean = Median = 1

• There is no data above 3 SD away from the mean

• The distribution is symmetric

• The Empirical Rule is always applicable

• The distribution is sometimes bimodal

A standard normal distribution:

• Always has a standard deviation of 1

• Is bell-shaped

• 95% of the data lies within 2 standard deviations of the mean

• Has a mean and median of 0

• All of the above

What fraction of the terms in a normal distribution have z-scores between -1.5 and 2.2?

• 0.8787

• 0.4861

• 0.9193

• 0.0529

What is the standard deviation of a normal distribution, whose mean is 22, in which an x-value of 36 has a z-score of 3.11?

• 4.5

• -4.5

• 1.495

• 0.523

Suppose you have a distribution that is approximately normal with a mean of 25 and a standard deviation of 1.4. If we were to replace each data point with its standardized value, what would the new mean and standard deviation be?

• 25 and 1.4

• 0 and 1

• 1 and 0

• Not enough information

Consider a normal distribution that has N(63,9) (that is, a mean of 63 and a standard deviation of 9). To the nearest integer, the percentile rank of a value of 50 in this distribution is:

• 7

• 20

• 16

• 93

Scores on a standard IQ test are normally distributed with a mean of 105 and a standard deviation of 18. To the nearest integer value, how high must your IQ be to fall within the top 2% of scores?

• 142

• 150

• 133

• 126

A set of 600 values is tested and determined to be normal. Its mean is 118 and its standard deviation is 24. Approximately how many terms can you expect to find between the values of 121 and 181? (Hint: there's an easy way and a hard way to do this. It's quicker to do it the easy way!)

• 268

• 332

• 451

• 589

• Not enough information

Consider normally distributed data with a mean of 85 and a standard deviation of 21. If there are 123 values between 56 and 63, approximately how many values are there in the distribution?

• 123

• 1234

• 1930

• 134

The weights of adult men in a hypothetical population are approximately normally distributed about a mean of 175 lbs. with a standard deviation of 15 lbs. If Harvey is at the 80th percentile in weight for adult men, his weight, in pounds, is closest to:

• 188

• 182

• 162

• 174