Statistics Homework

Missed Questions

Week 2 Quiz

#8. There are dozens of personality tests available on the World Wide Web. One test, scored on a scale of 0 to 200, is designed to give an indication of how “personable” the test taker is, with higher scores indicating more “personability.”

Suppose that scores on this test have a mean of 95 and a standard deviation of 24. Complete the following statements about the distribution of scores on this personality test

a. According to Chebyshev’s theorem, at least (what percentage) ______ of the score lie between 59 and 131

b. According to Chebyshev’s theorem, at least (what percentage_____ of the score lie between 47 and 143

c. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately (what percentage) of the scores lie between 47 and 143.

d. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the score lie between __ and ___

Week 2 Homework

#1 There are dozens of personality tests available on the World Wide Web. One test, scored on a scale of 0 to 200, is designed to give an indication of how “personable” the test taker is, with higher scores indicating more “personability.”

Suppose that scores on this test have a mean of 106 and a standard deviation of 19. Complete the following statements about the distribution of scores on this personality test

e. According to Chebyshev’s theorem, at least (what percentage) ______ of the score lie between 68 and 144

f. According to Chebyshev’s theorem, at least (what percentage_____ of the score lie between 77.5 and 134.5

g. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately (what percentage) of the scores lie between 68 and 144.

h. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the score lie between __ and ___

#2 A major cab company in Chicago has computed its mean fare form O’Hare Airport to the Drake Hotel to be $28.57, with a standard deviation of $3.21. Based on this information, complete the following statements about the distribution of the company’s fares from O’Hara Airport to the Drake Hotel.

a. According to Chebyshev’s theorem, at least 8/99 (about 89%) of the fares lie between __dollars and ____dollars. Round your answer to 2 decimals.

b. According to Chebyshev’s theorem, at least (what percentage_____ of the fares lie between 22.15 dollars and 34.99 dollars

c. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately (what percentage) of the fares lie between 22.15 dollars and 34.99 dollars

d. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the fares lie between __ dollars and ___ dollars

#8. An ordinary (fair) coin is tossed 3 times. Out comes are thus triples of “heads” and “tails” which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is tht, then R (tht) = 2. Suppose that the random variable X is definded in terms of R as follows: X -R² - R -1. The values of X are thus

Outcome	hht	thh	tht	tth	hhh	ttt	htt	hth
Value of X	-1	-1	1	1	-1	5	1	-1

#17- A new surgery is successful 85% of the time. If the results of 10 such surgeries are randomly sampled, what is the probability that more than 8 of them are successful? Carry your intermediate computation to at least four decimals places, and round your answers to two decimal places.

Week 1 Homework

#14 – The red blood cell counts (in 10²+³ cells per microliter) of a healthy adult measured on 6 days are follows:

52, 48, 49, 50, 55, 52

Find the standard deviation of this sample of counts Round your answer to two decimals places

#16 A investment company advertised that last year its clients, on average made a profit of 10%. If average refers to the mean, which of the following claims must be true based on this information

a. Two years ago, some of their clients made a profit of at least 10%

b. Last year all their clients made a profit of less than 17%

c. Last year at least one of their clients made a profit of exactly 10%

d. Last year fewer than half of their clients made a profit of 10% or less

e. Last year at least one of their clients made a profit of at least 10%

f. None of the above statements is true