Question 1

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university:
-Find the probability that none of the students voted.

Accepted Answer

The answer of In the most recent students' council election,...

Question 2

According to company records at a large firm,40% of all employees have a university degree.If six employees were selected at random from the company,what is the probability that none of the six has a university degree?

Accepted Answer

The answer of According to company records at a large...

Question 3

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university:
-Find the probability that exactly half voted in the election.

Accepted Answer

The probability of exactly half of the 20 students voting can be calculated using the binomial probability formula. With a voting probability of 0.19, the probability of exactly 10 out of 20 students voting is very low, resulting in approximately 0.0014.

Question 4

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%.
-If 100 calculators are selected at random,what is the expected number of defectives?

Accepted Answer

The expected number of defective calculators is calculated by multiplying the total number of calculators by the probability of finding a defective one. So, 100 calculators * 10% = 10 defective calculators.

Question 5

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%.
-If 3 calculators are selected at random,what is the probability that one of the calculators will be defective?

Accepted Answer

The answer of The J.O. Supplies Company buys calculators from...

Question 6

If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

Accepted Answer

The probability of getting a head on a single toss is 1/2. The probability of getting a head on three tosses is (1/2)^3 = 1/8. The expected winnings are 2 * (1/8) = $1/4.

Question 7

A large disaster cleaning company estimates that each of the jobs it bids on are finished within the bid time with probability 0.3 independent of each other job it bids on. Consider a random sample of 8 jobs that is has contracted.
-What is the probability that exactly 4 of the jobs were not completed within the bid time?

Accepted Answer

We can use the binomial probability formula: 
P(X=k) = nCk * p^k * (1-p)^(n-k)
where n is the number of trials, k is the number of successes, p is the probability of success, and (1-p) is the probability of failure.

In this case, n = 7, k = 4, p = 0.3 (since 30% of the jobs were not completed within the bid time), and (1-p) = 0.7.

Substituting these values into the formula, we get:
P(X=4) = 7C4 * 0.3^4 * 0.7^3
P(X=4) = 35 * 0.0081 * 0.343
P(X=4) = 0.0975

Therefore, the probability that exactly 4 of the jobs were not completed within the bid time is 0.0975, which is closest to option B: 1361.

Question 8

A class of 20 students;8 male and 12 female.If you select 8 students at random,what is the probability that at least 3 of them will be male?

Accepted Answer

The probability of selecting at least 3 males out of 8 students from a class of 20 (8 males and 12 females) can be calculated using the complementary probability of selecting 0, 1, or 2 males. The complementary probability involves calculating the probabilities of these three scenarios and subtracting them from 1. This approach simplifies the calculation, leading to the correct answer of 0.7404, which accounts for the various combinations of selecting at least 3 males in the group of 8 students.

Question 9

Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed according to Poisson distribution.
-Determine the probability of 6 patients arriving in a five-hour period.

Accepted Answer

The answer of Historical data shows that the average number...

Question 10

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to nearest whole number).

Accepted Answer

To find the mean for the number of defects in these groups of 160, we need to first find the probability of a chip being defective in the original sample, which is:

p = number of defective chips / total number of chips
p = 35 / (35 + 190) = 0.155

Now, we can use the formula for the mean of a binomial distribution:

mean = n*p

where n is the sample size and p is the probability of success (in this case, the probability of a chip being defective).

Substituting the given values, we get:

mean = 160 * 0.155 = 24.8

Rounding this to the nearest whole number, we get 25. Therefore, the best choice is D.

Question 11

If the probability distribution of X is:
$$\begin{array} { c c } 
\mathrm { X } & \mathrm { P } ( \mathrm { X } ) \
3 & 1 / 8 \
4 & 1 / 8 \
5 & 3 / 8 \
6 & 3 / 8
\end{array}$$
-What is the variance of X?

Accepted Answer

The answer of If the probability distribution of X is:
\[\begin{array}...

Question 12

A fair die is rolled 10 times.What is the probability that an odd number (1,3,or 5)will occur less than 3 times?

Accepted Answer

The probability of rolling an odd number on a fair die is 3/6 or 1/2. The probability of rolling an odd number less than 3 times in 10 rolls can be calculated by finding the probability of rolling 0, 1, or 2 odd numbers.

P(0 odds) = (1/2)^10 = 1/1024
P(1 odd) = 10*(1/2)^10 = 10/1024
P(2 odds) = 45*(1/2)^10 = 45/1024

Therefore, P(less than 3 odds) = P(0 odds) + P(1 odd) + P(2 odds) = 1/1024 + 10/1024 + 45/1024 = 56/1024 = 0.0547.

Option A) is the closest choice to this probability.

Question 13

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%.
-If 100 calculators are selected at random,what is the standard deviation of the number of defectives?

Accepted Answer

The standard deviation of a binomial distribution is given by the formula $\sigma = \sqrt{n \cdot p \cdot (1-p)}$, where $n$ is the number of trials (in this case, 100 calculators), and $p$ is the probability of success (in this case, the probability of a calculator being defective, which is 0.10). Plugging in the values, we get $\sigma = \sqrt{100 \cdot 0.10 \cdot (1-0.10)} = \sqrt{100 \cdot 0.10 \cdot 0.90} = \sqrt{9} = 3.0$.

Question 14

Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed according to Poisson distribution.
-Determine the probability of at least 4 but no more than 8 patients arriving in a three-hour period.

Accepted Answer

The answer of Historical data shows that the average number...

Question 15

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%.
-If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

Accepted Answer

The answer of The J.O. Supplies Company buys calculators from...

Question 16

If the probability distribution of X is:
$$\begin{array} { c c } 
\mathrm { X } & \mathrm { P } ( \mathrm { X } ) \
3 & 1 / 8 \
4 & 1 / 8 \
5 & 3 / 8 \
6 & 3 / 8
\end{array}$$
-What is the expected value of X?

Accepted Answer

The expected value (E) of X is calculated by summing the products of each value of X and its corresponding probability: E(X) = (3)(1/8) + (4)(1/8) + (5)(3/8) + (6)(3/8) = 3/8 + 4/8 + 15/8 + 18/8 = 40/8 = 5.

Question 17

Of all individual tax returns,37% include errors made by the taxpayer.If tax auditors are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.

Accepted Answer

The answer of Of all individual tax returns,37% include errors...

Question 18

A large disaster cleaning company estimates that each of the jobs it bids on are finished within the bid time with probability 0.3 independent of each other job it bids on. Consider a random sample of 8 jobs that is has contracted.
-What is the mean number of jobs completed within the bid time?

Accepted Answer

To find the mean number of jobs completed within the bid time, we need to divide the total number of jobs completed within the bid time by the number of contractors. 
Total number of jobs completed within the bid time = 72
Number of contractors = 30
Mean number of jobs completed within the bid time = 72/30 = 2.4 
Therefore, the best choice is C) 2.4.

Question 19

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.

Accepted Answer

The probability of guessing one correct answer is 1/5. So, the probability of guessing exactly four correct answers in a row is (1/5)^4. We need to account for all the 30 questions, but only four have to be correct, so we need to multiply by the number of ways of choosing 4 questions out of 30, which is denoted by "30 choose 4" (written as 30C4 or C(30,4)). Therefore, the probability of getting exactly four correct answers is:
(30C4) x (1/5)^4 x (4/5)^26 = 1325 x 0.01024 x 0.002843
= 0.03679 or approximately 0.037
Therefore, the best choice is B) 1325.

Question 20

In a study conducted for a local union,30% of the employees who became unemployed in the last year did so because they were laid off.Assume that we randomly select 10 employees who have recently left their position.Find the probability that exactly 4 of them were laid off.

Accepted Answer

The answer of In a study conducted for a local...

Quiz 4: Discrete Random Variables

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university: -Find the probability that none of the students voted.

According to company records at a large firm,40% of all employees have a university degree.If six employees were selected at random from the company,what is the probability that none of the six has a university degree?

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university: -Find the probability that exactly half voted in the election.

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 100 calculators are selected at random,what is the expected number of defectives?

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 3 calculators are selected at random,what is the probability that one of the calculators will be defective?

If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

A class of 20 students;8 male and 12 female.If you select 8 students at random,what is the probability that at least 3 of them will be male?

Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed according to Poisson distribution. -Determine the probability of 6 patients arriving in a five-hour period.

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to nearest whole number) .

If the probability distribution of X is: $\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$ -What is the variance of X?

A fair die is rolled 10 times.What is the probability that an odd number (1,3,or 5) will occur less than 3 times?

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 100 calculators are selected at random,what is the standard deviation of the number of defectives?

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

If the probability distribution of X is: $\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$ -What is the expected value of X?

Of all individual tax returns,37% include errors made by the taxpayer.If tax auditors are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.

A large disaster cleaning company estimates that each of the jobs it bids on are finished within the bid time with probability 0.3 independent of each other job it bids on. Consider a random sample of 8 jobs that is has contracted. -What is the mean number of jobs completed within the bid time?

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.

In a study conducted for a local union,30% of the employees who became unemployed in the last year did so because they were laid off.Assume that we randomly select 10 employees who have recently left their position.Find the probability that exactly 4 of them were laid off.

Quiz 4: Discrete Random Variables

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university: -Find the probability that none of the students voted.

According to company records at a large firm,40% of all employees have a university degree.If six employees were selected at random from the company,what is the probability that none of the six has a university degree?

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university: -Find the probability that exactly half voted in the election.

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 100 calculators are selected at random,what is the expected number of defectives?

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 3 calculators are selected at random,what is the probability that one of the calculators will be defective?

If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

A class of 20 students;8 male and 12 female.If you select 8 students at random,what is the probability that at least 3 of them will be male?

Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed according to Poisson distribution. -Determine the probability of 6 patients arriving in a five-hour period.

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to nearest whole number) .

If the probability distribution of X is: XP(X) 31/841/853/863/8\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}X3456​P(X) 1/81/83/83/8​ -What is the variance of X?

A fair die is rolled 10 times.What is the probability that an odd number (1,3,or 5) will occur less than 3 times?

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 100 calculators are selected at random,what is the standard deviation of the number of defectives?

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

If the probability distribution of X is: XP(X) 31/841/853/863/8\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}X3456​P(X) 1/81/83/83/8​ -What is the expected value of X?

Of all individual tax returns,37% include errors made by the taxpayer.If tax auditors are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.

A large disaster cleaning company estimates that each of the jobs it bids on are finished within the bid time with probability 0.3 independent of each other job it bids on. Consider a random sample of 8 jobs that is has contracted. -What is the mean number of jobs completed within the bid time?

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.

In a study conducted for a local union,30% of the employees who became unemployed in the last year did so because they were laid off.Assume that we randomly select 10 employees who have recently left their position.Find the probability that exactly 4 of them were laid off.

If the probability distribution of X is: $\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$ -What is the variance of X?

If the probability distribution of X is: $\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$ -What is the expected value of X?