Statistics Normal Calculations

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
How far did a male long jumper for State College jump if his jump was 1.68 standard deviations below the mean?

• 236.96 inches

• 239.48 inches

• 286.52 inches

• 289.04 inches

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 50th percentile.  How far did he jump?

• 0.50 inch

• 14 inches

• 50 inches

• 263 inches

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 75th percentile.  How long was his jump?

• 0.67 inch

• 263 inches

• 272.44 inches

• 277.25 inches

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.
What is the maximum distance a male longer jumper needs to jump to be in the bottom 10% of all male long jumpers from State College?

• 0.4602 inches

• 245.06 inches

• 280.94 inches

• 281.77 inches

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
What is the probability the next male long jumper from State College jumps between 240 and 262 inches?

• -42%

• 42%

• 57%

• 63%

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.
What is the minimum distance a male longer jumper needs to jump to be in the top 10% of all male long jumpers from State College?

• 0.4602 inches

• 245.06 inches

• 280.94 inches

• 281.77 inches

What is the mean starting salary?

• $30,000

• $30,533

• $32,500

• $32,533

• $35,000

Answer explanation

There are a total of 10 + 17 + 25 + 38 + 27 + 21 + 12 = 150 students. Their total salary is 10(15,000) + 17(20,000) + 25(25,000) + 38(30,000) + 27(35,000) + 21(40,000) + 12(45,000) = $4,580,000. The mean is 4,580,000/150 = $30,533

If the standard deviation of a set of observations is 0, you can conclude

• that there is no relationship between the observations.

• that the average value is 0.

• that all observations are the same value.

• that a mistake in arithmetic has been made.

• none of the above.

Answer explanation

Because of the squaring operation in the definition, the standard deviation (and also the variance) can be zero only if all the values in the set are equal.

Data on the number of text messages sent one weekend by junior and senior high school students in a large high school is summarized as follows: An AP Statistics student checking the calculations finds that the message counts for all the students were underreported by 5. When the numbers are corrected, what are the corrected IQR and standard deviation?

• IQR = 71 and standard deviation = 41.2

• IQR = 71 and standard deviation = 46.2

• IQR = 76 and standard deviation = 41.2

• IQR = 76 and standard deviation = 46.2

• IQR = 146 and standard deviation = 41.2

Answer explanation

Adding the same constant to every value will increase the Min, Q1, Median, Q3, Max, and Mean by that constant. However, measures of variability, including the IQR and the standard deviation, will remain unchanged.

Given that the median of a set is 350 and the interquartile range is 50, which of the following statements is true?

• Fifty percent of the data are less than or equal to 350.

• Fifty percent of the data are between 325 and 375.

• Seventy-five percent of the data are less than or equal to 375.

• The mean is between 325 and 375.

• All of the above statements are true.

Answer explanation

Fifty percent of the data are on either side of the median. The interquartile range gives the distance between Q1 and Q3 but doesn’t say where the median falls between Q1 and Q3. For example, it is possible that Q1 = 345 and Q3 = 395. Depending on the shape of the distribution, the mean could be anything.