A vending machine automatically pours soft drinks into cups

1 )The college student senate is sponsoring a spring break Caribbean cruise raffle. The proceeds are to be donated to the Samaritan Center for the Homeless. A local travel agency donated the cruise, valued at $2000. The students sold 2544 raffle tickets at $5 per ticket.

(a) Kevin bought thirty-two tickets. What is the probability that Kevin will win the spring break cruise to the Caribbean? (Round your answer to five decimal places.)

What is the probability that Kevin will not win the cruise? (Round your answer to five decimal places.)

(b) Expected earnings can be found by multiplying the value of the cruise by the probability that Kevin will win. What are Kevin's expected earnings? (Round your answer to two decimal places.)

$

Is this more or less than the amount Kevin paid for the thirty-two tickets?

How much did Kevin effectively contriute to the Samaritan Center for the Homeless? (Round your answer to two decimal places.)

2 Raul received a score of 76 on a history test for which the class mean was 70 with a standard deviation of 7. He received a score of 76 on a biology test for which the class mean was 70 with standard deviation 7. On which test did he do better relative to the rest of the class?

3) In the binomial probability distribution, let the number of trials be n = 4, and let the probability of success be p = 0.3688. Use a calculator to compute the following.

(a) The probability of three successes. (Round your answer to three decimal places.)

(b) The probability of four successes. (Round your answer to three decimal places.)

(c) The probability of three or four successes. (Round your answer to three decimal places.)

4) The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 15% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of eight adult friends, what is the probability of the following? (Round your answers to three decimal places.)

(a) no one has done a one-time fling

(b) at least one person has done a one-time fling

(c) no more than two people have done a one-time fling

5) A research team conducted a study showing that approximately 20% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)

(a) at least one tie is too tight

(b) more than two ties are too tight

(c) no tie is too tight

(d) at least 18 ties are not too tight

6) Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey, 47% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability of the following.

(a) Out of five adults, none is concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

(b) Out of five adults, all are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

(c) Out of five adults, exactly three are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

7) Tree-ring dates were used extensively in archaeological studies at Burnt Mesa Pueblo. At one site on the mesa, tree-ring dates (for many samples) gave a mean date of μ1 = year 1276 with standard deviation σ1 = 36 years. At a second, removed site, the tree-ring dates gave a mean of μ2 = year 1109 with standard deviation σ2 = 36 years. Assume that both sites had dates that were approximately normally distributed. In the first area, an object was found and dated as x1 = year 1220. In the second area, another object was found and dated as x2 = year 1249.

(a) Convert both x1 and x2 to z values, and locate both of these values under the standard normal curve of the figure above. (Round your answers to two decimal places.)

z1 =

z2 =

(b) Which of these two items is the more unusual as an archaeological find in its location?

x1; the further a z value is from zero, the more unusual it is.

x2; the further a z value is from zero, the more unusual it is.

x1; the closer a z value is to zero, the more unusual it is.

x2; the closer a z value is to zero, the more unusual it is.

8) The incubation time for Rhode Island Red chicks is normally distributed with a mean of 26 days and standard deviation of approximately 2 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.)

(a) in 22 to 30 days

chicks

(b) in 24 to 28 days

chicks

(c) in 26 days or fewer

chicks

(d) in 20 to 32 days

Chicks

9) A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6 ounces and standard deviation of 0.4 ounce. Examine the figure below and answer the following questions.

(a) Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to two decimal places.)

(b) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer to two decimal places.)

(c) The machine has just been loaded with 864 cups. How many of these do you expect will overflow when served?