Mathematics

Question 11 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.  Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.  For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.  If 1.5% of the bolts made by an automotive factory are defective, what is the probability that in a shipment of 200 bolts, there are 6 defective bolts? Place your answer, rounded to four decimal places, in the blank.

Question 12 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.  Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.  For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months.

x 0 1 2 3 4 5 6
P (X=x) 0.55 0.15 0.10 0.10 0.04 0.03 0.03

What is the variance of X?  Place your answer, rounded to two decimal places in the blank. For example, 4.56 would be a legitimate entry.

Question 13 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.  Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.  For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

If a gambler rolls two dice and gets a sum of four, he wins $10; and if he gets a sum of three, he wins $25. The cost to play the game is $5. What is the expectation of this game?

 

Place your answer, rounded to two decimal places, in the blank.     When entering your answer do not use a dollar sign. However, if the expected payoff is negative be sure to use a minus sign. For example, -1.23 would be a legitimate entry.

Question 14 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.  Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.  For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question.

 

  Number of Products Purchased  
Brands Purchased Fewer Same More Total
Same 10 14 24 48
Changed 262 82 8 352
Total 272 96 32 400

Given that a consumer changed brands, what then is the probability that the consumer purchased fewer products than before? Place your answer, rounded to 4 decimal places, in the blank.

Part 4 of 6 –
Question 15 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.  Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.  For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.  The president of a bank is attempting to arrange a meeting with the three vice presidents for a Friday weekly meeting. He believes that each of these three busy individuals, independently of the others, has about 40% chance of being able to attend the meeting. What is the probability that at least two of the three vice presidents can attend the meeting? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 would be a legitimate entry.

Question 16 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.  Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.  For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Mothers Against Drunk Driving (MADD) is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

                                                         Number of Vehicles Involved

Did alcohol play a role? 1 2 3
Yes 60 110 30 200
No 40 215 45 300
  100 325 75

Given that multiple vehicles were involved, what proportion of accidents involved alcohol?

 

Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry.

Question 17 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.  Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.  For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

f$A_{1}f$ = chocolate chosen

f$A_{2}f$ = strawberry chosen

f$A_{3}f$ = vanilla chosen

f$Bf$ = ice cream on a cone

f$ar{B}=f$ice cream in a cup Find the probability that the ice cream was strawberry flavor, given that it was sold on a cone. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.

Question 18 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.  Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.  For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.  The president of a bank is attempting to arrange a meeting with the three vice presidents for a Friday weekly meeting. He believes that each of these three busy individuals, independently of the others, has about 40% chance of being able to attend the meeting. If the meeting will be held only if every vice president can attend, what is the probability that the meeting will take place? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 would be a legitimate entry.

Part 5 of 6 –
Question 19 of 20

Jim and Mike go to a coffee shop during their lunch break and toss a coin to see who will pay. The probability that Mike will pay three days in a row is 0.125.

 True
 False
Part 6 of 6 –
Question 20 of 20

True or False: The probability of a success must remain the same for each trial in a binomial experiment.

 True
 False

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