Mr. Hansen
Quiz Questions from Chapter 2

Name: ____________________________

Instructions: Show sufficient work for each problem. Remember to show me the formula, show me the plug-ins, and show me the answer.

 

For questions A1-A4, think about a density curve that consists of a straight line segment from the point (0, 2/3) to the point (1, 4/3) in the x-y plane.

A1.

Sketch this density curve.
A2.

What percentage of the observations lie below 1/2?
A3.

What percentage of the observations lie below 1?
A4.

What percentage of the observations lie between 1/2 and 1?

 

For questions A5-A7, the scores of a reference population on the Wechsler Intelligence Scale for Children (WISC) are known to be normally distributed with m = 100 and s = 15.
A5.

What score would represent the 50th percentile? Explain.

A6.

Approximately what percentage of the scores fall in the range from 70 to 130?
A7.

A score in what range would represent the top 16% of the scores?

 

For questions B1-B4, a density curve consists of a straight line segment that begins at the origin (0, 0) and has slope 1.
B1.

Sketch this density curve. What are the coordinates of the right endpoint of the segment? (Note that the right endpoint should be fixed so that the total area under the curve is 1. This is required for a valid density curve.)
B2.

Determine the median, the first quartile (Q1), and the third quartile (Q3).
B3.

Relative to the median, where would you expect the mean of the distribution to lie?
B4.

What percentage of the observations lie below 0.5? Above 1.5?
 

For questions B5 and B6, Runner’s World reports that the times of the finishers in the New York City 10-km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes.
B5.

Find the proportion of runners who take more than 70 minutes to finish.
B6.

Find the proportion of runners who finish in less than 43 minutes.
C1.

A study of elite distance runners reported the mean weight to be 63.1 kg with a standard deviation of 4.8 kg. Assuming that the distribution of weights is normal, sketch the density curve of the weight distribution, with the horizontal axis marked in kilograms.
C2.

Jill scores 680 on the mathematics part of the SAT. The distribution of SAT scores in a certain population is normally distributed with mean 500 and standard deviation 100. Jack takes the ACT mathematics test and scores 27. ACT scores are normally distributed with mean 18 and standard deviation 6. Find the standardized scores for both students.
C3.

In question C2, assuming that both tests measure the same kind of ability, who has the higher score?
 

Use Table A or your calculator to answer questions C4 and C5. In each case, find the proportion of observations from a standard normal distribution that satisfies the given condition, and shade the area under the standard normal curve that is the answer to the question.
C4.

Z < –1.5
C5.

–1.5 < Z < 0.8