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Exam 6: Probability in Statistics

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Question 31

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If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?

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Question 32

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The distribution of B.A. degrees conferred by a local college is listed below, by major. $\begin{array} { l r } { \underline { \text { Major } } } & \underline { \text { Frequenc }} \\\text { English } & 2073 \\\text { Mathematics } & 2164 \\\text { Chemistry } & 318 \\\text { Physics } & 856 \\\text { Liberal Arts } & 1358 \\\text { Business } & 1676 \\\text { Engineering } & \underline { 868 } \\& 9313\end{array}$ What is the probability that a randomly selected degree is not in Business?

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Question 33

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In the first series of rolls of a die, the number of odd numbers exceeded the number of even numbers by 5. In the second series of rolls of the same die, the number of odd numbers exceeded the number of even numbers by 11. Determine which series is closer to the 50/50 ratio of odd/even expected of a fairly rolled die.

Wisconsin has 72 counties. The names of six of them begin with the letter C. Is it "significant" for a randomly chosen Wisconsin county to be one of those six counties.

The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000. $\begin{array} { r r r r r r r r r r } 112,000 & 126,000 & 90,000 & 133,000 & 94,000 & 112,000 & 98,000 & 82,000 & 147,000 & 182,000 \\86,000 & 105,000 & 140,000 & 94,000 & 126,000 & 119,000 & 98,000 & 154,000 & 78,000 & 119,000\end{array}$

100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the transportation results. If one of the 100 employees is randomly selected, find the probability that the person does not commute by public transportation. A) Public transportation: 7 full-time, 8 part-time B) Bicycle: 3 full-time, 4 part-time C) Drive alone: 29 full-time, 34 part-time D) Carpool: 9 full-time, 6 part-time

A 28-year-old man pays $125 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, to the nearest dollar, what is the man's expected value for the insurance policy?

Suppose that you pay $2 to roll the die in Problem 13 with the understanding that you will receive $6 if it comes up a 1 or a 3, but nothing otherwise. What is your expected value?

In 2003, the U.S. death rate was 1.2 per 100,000 people due to motorcycle accidents. Motorcycles in the U.S. were involved in fatal crashes at the rate of 35.0 per 100 million miles driven. If the population of the U.S. is 300,000,000, what is the expected number of deaths due to motorcycle accidents?

The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number living out of an original 100,000, and the additional life expectancy for a person of that age. Exact Male Female P(Death Additional P(Death Additional Age. $\begin{array}{c}\quad\quad\quad\quad\quad\quad\text { Male } \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Female }\\\begin{array}{|c|c|c|c|c|c|c|}\hline{\text {Exact Age }} & \begin{array}{c}\text { P(Death } \\\text { within one } \\\text { year) }\end{array} & \begin{array}{c}\text { Number of } \\\text { Living }\end{array} & \begin{array}{c}\text { Additional } \\\text { Life } \\\text { Expectancy }\end{array} & \begin{array}{c}\text { P(Death } \\\text { within one } \\\text { year) }\end{array} & \begin{array}{c}\text { Number of } \\\text { Living }\end{array} & \begin{array}{c}\text { Additional } \\\text { Life } \\\text { Expectancy }\end{array} \\\hline 10 & 0.000111 & 99,021 & 65.13 & 0.000105 & 99,217 & 70.22 \\\hline 20 & 0.001287 & 98,451 & 55.46 & 0.000469 & 98,950 & 60.40 \\\hline 30 & 0.001375 & 97,113 & 46.16 & 0.000627 & 98,431 & 50.69 \\\hline 40 & 0.002542 & 95,427 & 36.88 & 0.001498 & 97,513 & 41.11 \\\hline 50 & 0.005696 & 91,853 & 28.09 & 0.003240 & 95,378 & 31.91 \\\hline 60 & 0.012263 & 84,692 & 20.00 & 0.007740 & 90,847 & 23.21 \\\hline 70 & 0.028904 & 70,214 & 12.98 & 0.018938 & 80,583 & 15.45 \\\hline 80 & 0.071687 & 44,272 & 7.43 & 0.049527 & 59,341 & 9.00 \\\hline 90 & 0.188644 & 12,868 & 3.68 & 0.146696 & 24,331 & 4.45 \\\hline\end{array}\end{array}$ To what age may a male of age 70 expect to live on the average?

A study of two types of weed killers was done on two identical weed plots. One weed killer killed 15% more weeds than the other. This difference was significant at the 0.05 level. What Does this mean?

On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

state whether there is one way for the given observation to occur (outcome) or more than one way for the given observation to occur (in which case it is an event) . -Drawing three queens from a regular deck of cards

In a poll, respondents were asked whether they had ever been in a car accident. respondents indicated that they had been in a car accident and 370 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth.

Suppose that you have a loaded die for which the probabilities of the numbers 1 through 6 are given below. $\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Probability } & 1 / 21 & 4 / 21 & 6 / 21 & 2 / 21 & 3 / 21 & 5 / 21 \\\hline\end{array}$ If you roll this die 630 times, how many times should you expect to see a 1 or a 2?

Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?

The advertising for a cold remedy claimed that no other cold remedy acted faster. In a experiment to compare that remedy with another one, it did act faster on average, but the result was not significant. What does this mean?

Is it "significant" to get a total of 2 when a pair of dice is rolled.

Assume that a study of 500 randomly selected school bus routes showed that 480 arrived on time. Is it "significant" for a school bus to arrive late.

If you are told that a mystery person's birthday is in February, would it be "significant" to guess that person's birth date (not including the year).