Question 1

Use the following information for questions:
 The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes.
-What is the probability that a randomly chosen student will complete the exam in 30 minutes or less?

Accepted Answer

To find the probability that a student completes the exam in 30 minutes or less, we calculate the Z-score for X = 30 using the formula Z = (X - mean) / standard deviation = (30 - 60) / 30 = -1. The probability corresponding to Z = -1 (looking up in a standard normal distribution table or using a calculator) is approximately 0.1587. This means there's a 15.87% chance a student will finish in 30 minutes or less.

Question 2

Use the following information for questions:
 The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes.
-What is the probability that a randomly chosen student will take at least an hour to complete the exam?

Accepted Answer

The answer of Use the following information for questions:
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Question 3

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -By what time should 67% of the students have finished the exam? (i.e. What is the 67^th percentile for X?)

Accepted Answer

The 67th percentile in a normal distribution corresponds to a Z-score of approximately 0.44 (from Z-tables or standard normal distribution tables). Using the formula for converting Z-scores to raw scores: X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the Z-score, we get X = 60 + 0.44(30) = 60 + 13.2 = 73.2 minutes.

Question 4

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -By what time should 99% of the students have finished the exam? (i.e. What is the 99^th percentile for X?)

Accepted Answer

To find the 99th percentile of a normal distribution, we use the Z-score formula associated with the 99th percentile, which is approximately 2.33 (from standard normal distribution tables). The formula to convert a Z-score to an X value in a normal distribution is X = μ + Zσ, where μ is the mean and σ is the standard deviation. Plugging in the values: X = 60 + 2.33(30) = 60 + 69.9 = 129.9 minutes. This means that by 129.9 minutes, 99% of the students should have finished the exam.

Question 5

The number of first-year students who will decide to live in dormitories is a binomial random variable X with n = 1000 and p = 0.50. Use the normal approximation with continuity correction to approximate the probability that X will be no more than 490, P(X $\leq$ 490).

Accepted Answer

The normal approximation with continuity correction is given by:P(X $\leq$ 490) = P(Z $\leq$ (490 - 500) / sqrt(1000 * 0.50 * 0.50)) = P(Z $\leq$ -1) = 0.1587Using the continuity correction, we add 0.5 to the upper limit of the interval, which gives us:P(X $\leq$ 490) = P(Z $\leq$ (490.5 - 500) / sqrt(1000 * 0.50 * 0.50)) = P(Z $\leq$ -0.99) = 0.1587Therefore, the probability that X will be no more than 490 is 0.1587.

Question 6

The normal approximation to the binomial distribution is most useful for finding which of the following?

Accepted Answer

The normal approximation to the binomial distribution is most useful for finding the probability P(X ≤ k) when X is a binomial random variable with a large number of trials (n). This approximation simplifies calculations for large n, where using the binomial formula directly would be cumbersome.

Question 7

Suppose that in a large population, the proportion that is left-handed is p = 0.10. Suppose n = 20 people will be randomly selected and X = number of people in the sample who are left-handed. What probability model should be used to find the probability that X = 3?

Accepted Answer

The binomial probability model is appropriate because we have a fixed number of independent trials (n = 20), each trial has only two possible outcomes (left-handed or not left-handed), and the probability of success (being left-handed, p = 0.10) is the same for each trial.

Question 8

Suppose that a quiz consists of 20 True-False questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with True and False equally likely). How would you find the probability that the will student get 8 or fewer answers correct?

Accepted Answer

The correct approach is to use a binomial distribution because the scenario involves a fixed number of independent trials (20 True-False questions), each with two possible outcomes (True or False), and the probability of success (guessing correctly) is constant (0.5). The cumulative probability for getting 8 or fewer correct answers involves summing the probabilities of getting 0, 1, 2, ..., 8 correct answers, which is what option D suggests.

Question 9

Use the following information for questions:
 Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes.
-What proportion of customers is expected to wait more than 6 minutes?

Accepted Answer

The answer of Use the following information for questions:
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Question 10

Use the following information for questions:
 Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes.
-Complete the sentence: About 25% of the customers are expected to wait at most ____ minutes?

Accepted Answer

The answer of Use the following information for questions:
 Suppose...

Question 11

Use the following information for questions:
 Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes.
-What is the expected waiting time?

Accepted Answer

The answer of Use the following information for questions:
 Suppose...

Question 12

Use the following information for questions:
 Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes.
-What is the interquartile range for waiting time?

Accepted Answer

The answer of Use the following information for questions:
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Question 13

Use the following information for questions:
 Some managers of companies use employee rankings to laud the best and let go of the worst. Suppose the distribution of rankings of employees at a large company is normal with a mean of 65 points and a standard deviation of 6 points.
-What proportion of employees has a ranking above 59 points?

Accepted Answer

The answer of Use the following information for questions:
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Question 14

Use the following information for questions:
 Some managers of companies use employee rankings to laud the best and let go of the worst. Suppose the distribution of rankings of employees at a large company is normal with a mean of 65 points and a standard deviation of 6 points.
-Managers at this large company were told to determine the top 20 percent, the bottom 10 percent and the remaining 70 percent in the middle, and then "weed out" (let go) those in that bottom tier. Using the provided model for rankings, what is the cut-off for an employee to be in the top 20 percent?

Accepted Answer

The answer of Use the following information for questions:
 Some...

Question 15

Use the following information for questions:
 Some managers of companies use employee rankings to laud the best and let go of the worst. Suppose the distribution of rankings of employees at a large company is normal with a mean of 65 points and a standard deviation of 6 points.
-Using the provided model for rankings, what is the cut-off for an employee to be "weeded out?"

Accepted Answer

The answer of Use the following information for questions:
 Some...

Question 16

Use the following information for questions:
 The time to complete an exam for a randomly chosen student in a textiles class is a normal random variable with a mean of 50 minutes and a standard deviation of 10 minutes.
-What percent of the class will have finished the exam by 75 minutes?

Accepted Answer

The answer of Use the following information for questions:
 The...

Question 17

Use the following information for questions: The time to complete an exam for a randomly chosen student in a textiles class is a normal random variable with a mean of 50 minutes and a standard deviation of 10 minutes. -At what time will 75% of the class have finished the exam? (i.e. What is the 75^th percentile of the distribution?)

Accepted Answer

The answer of Use the following information for questions:
 The...

Question 18

Use the following information for questions:
 Suppose X is a binomial random variable with n = 800 and p = 0.20.
-Find the expected value E(X).

Accepted Answer

The answer of Use the following information for questions:
 Suppose...

Question 19

Use the following information for questions:
 Suppose X is a binomial random variable with n = 800 and p = 0.20.
-Find the approximate the probability P(X ≥ 180) with the normal approximation with a continuity correction.

Accepted Answer

The answer of Use the following information for questions:
 Suppose...

Question 20

Use the following information for questions:
 According to the National Education Association, the country's largest teachers union, the proportion of men in teaching is at its lowest level in 40 years. Only 21 percent of teachers in U.S. public schools are men. In early grades, the gender ratio is even more imbalanced - just 9 percent of elementary school teachers are men. Suppose we randomly select 120 teachers who work in U.S. public schools
-How many men would we expect to find in the sample of 120 teachers?

Accepted Answer

The answer of Use the following information for questions:
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Quiz 8: Random Variables

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -What is the probability that a randomly chosen student will complete the exam in 30 minutes or less?

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -What is the probability that a randomly chosen student will take at least an hour to complete the exam?

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -By what time should 67% of the students have finished the exam? (i.e. What is the 67^th percentile for X?)

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -By what time should 99% of the students have finished the exam? (i.e. What is the 99^th percentile for X?)

The number of first-year students who will decide to live in dormitories is a binomial random variable X with n = 1000 and p = 0.50. Use the normal approximation with continuity correction to approximate the probability that X will be no more than 490, P(X $\leq$ 490) .

The normal approximation to the binomial distribution is most useful for finding which of the following?

Suppose that in a large population, the proportion that is left-handed is p = 0.10. Suppose n = 20 people will be randomly selected and X = number of people in the sample who are left-handed. What probability model should be used to find the probability that X = 3?

Suppose that a quiz consists of 20 True-False questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with True and False equally likely) . How would you find the probability that the will student get 8 or fewer answers correct?

Use the following information for questions: Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. -What proportion of customers is expected to wait more than 6 minutes?

Use the following information for questions: Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. -Complete the sentence: About 25% of the customers are expected to wait at most ____ minutes?

Use the following information for questions: Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. -What is the expected waiting time?

Use the following information for questions: Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. -What is the interquartile range for waiting time?

Use the following information for questions: The time to complete an exam for a randomly chosen student in a textiles class is a normal random variable with a mean of 50 minutes and a standard deviation of 10 minutes. -What percent of the class will have finished the exam by 75 minutes?

Use the following information for questions: Suppose X is a binomial random variable with n = 800 and p = 0.20. -Find the expected value E(X).

Use the following information for questions: Suppose X is a binomial random variable with n = 800 and p = 0.20. -Find the approximate the probability P(X ≥ 180) with the normal approximation with a continuity correction.

Quiz 8: Random Variables

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -What is the probability that a randomly chosen student will complete the exam in 30 minutes or less?

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -What is the probability that a randomly chosen student will take at least an hour to complete the exam?

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -By what time should 67% of the students have finished the exam? (i.e. What is the 67th percentile for X?)

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -By what time should 99% of the students have finished the exam? (i.e. What is the 99th percentile for X?)

The number of first-year students who will decide to live in dormitories is a binomial random variable X with n = 1000 and p = 0.50. Use the normal approximation with continuity correction to approximate the probability that X will be no more than 490, P(X ≤\leq≤ 490) .

The normal approximation to the binomial distribution is most useful for finding which of the following?

Suppose that in a large population, the proportion that is left-handed is p = 0.10. Suppose n = 20 people will be randomly selected and X = number of people in the sample who are left-handed. What probability model should be used to find the probability that X = 3?

Suppose that a quiz consists of 20 True-False questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with True and False equally likely) . How would you find the probability that the will student get 8 or fewer answers correct?

Use the following information for questions: Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. -What proportion of customers is expected to wait more than 6 minutes?

Use the following information for questions: Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. -Complete the sentence: About 25% of the customers are expected to wait at most ____ minutes?

Use the following information for questions: Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. -What is the expected waiting time?

Use the following information for questions: Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. -What is the interquartile range for waiting time?

Use the following information for questions: The time to complete an exam for a randomly chosen student in a textiles class is a normal random variable with a mean of 50 minutes and a standard deviation of 10 minutes. -What percent of the class will have finished the exam by 75 minutes?

Use the following information for questions: Suppose X is a binomial random variable with n = 800 and p = 0.20. -Find the expected value E(X).

Use the following information for questions: Suppose X is a binomial random variable with n = 800 and p = 0.20. -Find the approximate the probability P(X ≥ 180) with the normal approximation with a continuity correction.

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -By what time should 67% of the students have finished the exam? (i.e. What is the 67^th percentile for X?)

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -By what time should 99% of the students have finished the exam? (i.e. What is the 99^th percentile for X?)

The number of first-year students who will decide to live in dormitories is a binomial random variable X with n = 1000 and p = 0.50. Use the normal approximation with continuity correction to approximate the probability that X will be no more than 490, P(X $\leq$ 490) .