Answers to quiz 3

Round z-scores to two places after the decimal. Round proportions to four places after the decimal.

(6 points) The heights of men as a population is normally distributed, with mux= 69.0” and sigmax= 2.8”.

What is the z-score for 5’6”? ANSWER: -1.07
What proportion does this correspond to? ANSWER: .1423 (TI-83 ANSWER: .1420)

What is the z-score for 6’0”?
What proportion does this correspond to? ANSWER: .8577 (TI-83 ANSWER: .8580)

What percentage of men are between 5’6” and 6’0”? ANSWER: .7154 (TI-83 ANSWER: .7160)

(6 points) Assume we have a data set where mux= 10 and sigmax= 2.5. Use the Central Limit Theorem formula to find the answers to the following questions.

What is the z-score of a sample where x-bar = 8.3 and n = 12 and what proportion does it correspond to?

z-score = ANSWER: -2.36
proportion = ANSWER: .0091

Thanks to Daniel Barreto for pointing out my error in the first answer I posted.

What is the z-score of a sample where x-bar = 10.2 and n = 40 and what proportion does it correspond to?

z-score = ANSWER: 0.51
proportion = ANSWER: .6950 (TI-83 ANSWER: .6936)

What proportion does x = 13 correspond to? (Single sample)
Answer: .8849

(8 points) Consider the number of theaters list on the blue handout. Find the number of units in each category, f(x) and find the relative frequency p(x) = f(x)/n for each of these numerical intervals. Write relative frequency as percentages. Draw a horizontal bar chart using the template provided.

Interval ___ frequency relative frequency

Under 3500 10_________40%

3500-4000 7__________28%

Over 4000 8 __________32%

__________0%-------10%------20%------30%---------40%

Under 3500XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

3500-4000_XXXXXXXXXXXXXXXXXXXXXXXXXXX

Over 4000_XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX