Question 1

Would it be "significant" to guess the day of the week of a person's birth.

Accepted Answer

Guessing the day of the week of a person's birth is not significant because there are only seven possible options, making it a random guess with a 1 in 7 chance of being correct.

Question 2

Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 5 or a 2, nothing otherwise. What is your expected value?
A) $1.00
B) $0.00
C) $3.00
D) −$1.00

Accepted Answer

The probability of rolling a 5 or a 2 is 2/6 = 1/3. The expected value is (1/3 * $3) + (2/3 * $0) - $1 = $1 - $1 = $0.

Question 3

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?

Accepted Answer

82.98

Question 4

Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. He reshuffled the cards and dealt 30 cards. This time, the number of red cards exceeded the number of black cards by 10. Determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.
A) The first series is closer because 1/10 is farther from 1/2 than is 1/8.
B) The series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.
C) The second series is closer because 20/30 is closer to 1/2 than is 14/20.
D) The first series is closer because the difference between red and black is smaller than the difference in the second series.

Accepted Answer

The answer of Joe dealt 20 cards from a standard...

Question 5

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).
-Rolling at least one 6 with two fair dice
A) Outcome
B) Event

Accepted Answer

Rolling at least one 6 with two dice can occur in multiple ways, such as rolling a 6 on the first die or the second die, or both, making it an event.

Question 6

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).
-Tossing two tails with three fair coins
A) Outcome
B) Event

Accepted Answer

There are multiple ways to achieve two tails when tossing three coins, such as HTT, THT, and TTH, making it an event.

Question 7

A study of 600 college students taking Statistics 101 revealed that 54 students received the grade of A. Typically 10% of the class gets an A. The difference between this group of students and the expected value is not significant at the 0.05 level. What does this mean in this case?
A) The probability that the difference occurred due to chance is less than 0.05.
B) The probability of getting an A is 10% and only 9% got an A in this study. The difference is less than 5% so it is not significant.
C) There is not enough information to make any conclusion.
D) The probability that the difference occurred due to chance is more than 0.05.

Accepted Answer

The statement means that the observed difference between the actual percentage of students who got an A (9%) and the expected percentage (10%) is not statistically significant, implying that the probability of this difference occurring by chance is greater than 0.05.

Question 8

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.

Accepted Answer

The study shows that only 20 out of 500 buses arrived late, which is 4%. This low percentage suggests that it is statistically significant for a bus to arrive late, as it is an infrequent event.

Question 9

Is it "significant" to get an 11 when a pair of dice is rolled.

Accepted Answer

The answer of Is it "significant" to get an 11...

Question 10

A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.)

Accepted Answer

The answer of A committee of three people is to...

Question 11

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?

Accepted Answer

The answer of The distribution of B.A. degrees conferred by...

Question 12

Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.413. Find the probability that in a given year it will not snow on January 1st in that town.

Accepted Answer

The answer of Based on meteorological records, the probability that...

Question 13

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at most one head?

Accepted Answer

The answer of If you flip a coin three times,...

Question 14

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

Accepted Answer

A total of 2 is significant because it is the least likely outcome when rolling two dice, with only one possible combination (1,1) out of 36 total combinations, giving it a probability of 1/36.

Question 15

A study of students taking Statistics 101 was done. Four hundred students who studied for more than 10 hours averaged a B. Two hundred students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 level. What does this mean?
A) The probability that the difference was due to chance alone is greater than 0.01.
B) There is less than a 0.01 chance that the first group's grades were better by chance alone.
C) The improvement was due to the fact that more people studied.
D) There is not enough information to make any conclusion.

Accepted Answer

There is less than a 0.01 chance that the first group's grades were better by chance alone.

Question 16

Suppose you have an extremely unfair coin: The probability of a head is 1/3 and the probability of a tail is 2/3. If you toss the coin 72 times, how many heads do you expect to see?

Accepted Answer

The answer of Suppose you have an extremely unfair coin:...

Question 17

A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

Accepted Answer

The answer of A bag contains 4 red marbles, 3...

Question 18

From the table in Problem 16, how many 70-year old females on average will be living at age 71?

Accepted Answer

The answer of From the table in Problem 16, how...

Question 19

A sample space consists of 46 separate events that are equally likely. What is the probability of each?

Accepted Answer

The answer of A sample space consists of 46 separate...

Question 20

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.
 $$\begin{array} { r r r r r r r r r r } 
112,000 & 126,000 & 90,000 & 133,000 & 94,000 & 112,000 & 98,000 & 82,000 & 147,000 & 182,000 \
86,000 & 105,000 & 140,000 & 94,000 & 126,000 & 119,000 & 98,000 & 154,000 & 78,000 & 119,000
\end{array}$$

Accepted Answer

The answer of The data set represents the income levels...

Quiz 6: Probability in Statistics

Would it be "significant" to guess the day of the week of a person's birth.

Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 5 or a 2, nothing otherwise. What is your expected value?

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) . -Rolling at least one 6 with two fair dice

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) . -Tossing two tails with three fair coins

A study of 600 college students taking Statistics 101 revealed that 54 students received the grade of A. Typically 10% of the class gets an A. The difference between this group of students and the expected value is not significant at the 0.05 level. What does this mean in this case?