BSTAT REVIEW 2305 SECOND EXAM

On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What is the probability that two light bulbs will be defective? A.) 0.0105 B) 0.5987 C.) 0.3151 D.) 0.0746

0.0746

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective? A-0.6561 B-0.0010 C-0.2916 D-0.3439

0.3439

On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What are the mean and variance of the number of defective bulbs? A-0.50 and 0.6892 B-0.50 and 0.475 C-0.475 and 0.6892 D-0.475 and 0.475

0.50 and 0.475

According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries. Suppose seven expectant mothers are randomly selected. What is the probability that at least one of the expectant mothers will have a Caesarean delivery? A-0.9394 B-0.0606 C-0.9742 D-0.2090

0.9394

According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries. Suppose seven expectant mothers are randomly selected. What is the standard deviation of the number of mothers who will have a Caesarean delivery? A-1.24 B-4.69 C-2.31 D-1.54

1.24

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. Professor Elderman offers his class of 36 a pizza party if the class average is above 80. What is the probability that he will have to deliver on his promise? A) 0.0228 B) 0.9772 C) 0.3707 D) 0.6293

A) 0.0228

Find the probability P(−1.96 ≤ Z ≤ 0). A) 0.4750 B) 0.5250 C) 0.0250 D) 0.0500

A) 0.4750

Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. The probability that the sample mean is less than 30 school days is ______. A) 0.9088 B) 0.4129 C) 0.5871 D) 0.0918

A) 0.9088

An investment consultant tells her client that the probability of making a positive return with her suggested portfolio is 0.90. What is the risk, measured by standard deviation that this investment manager has assumed in her calculation if it is known that returns from her suggested portfolio are normally distributed with a mean of 6%? A) 4.69% B) 1.28% C) 6.00% D) 10.0%

A) 4.69%

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 16) related to P(X < 16)? A) P(X > 16) is greater than P(X < 16). B) No comparison can be made with the given information. C) P(X > 16) is smaller than P(X < 16). D) P(X > 16) is the same as P(X < 16).

A) P(X > 16) is greater than P(X < 16).

If X has a normal distribution with µ = 100 and σ = 5, then the probability P(90 ≤ X ≤ 95) can be expressed in terms of a standard normal variable Z as ______. A) P(−2 ≤ Z ≤ −1) B) P(−2 ≤ Z ≤ −2) C) P(−2 ≤ Z ≤ 1) D) P(2 ≤ Z ≤ 1)

A) P(−2 ≤ Z ≤ −1)

Using the central limit theorem, applied to the sampling distribution of the sample proportion, what conditions must be met? A) np≥5np≥5 and n(1−p ) ≥ 5n(1⁢−p⁢ ) ≥ 5 B) np≤5np≤5 and n(1−p ) ≤ 5n(1⁢−p⁢ ) ≤ 5 C) np≥5np≥5 and n(1−p ) ≤ 5n(1⁢−p⁢ ) ≤ 5 D) np≤5np≤5 and n(1−p ) ≥ 5

A) np≥5np≥5 and n(1−p ) ≥ 5n(1⁢−p⁢ ) ≥ 5

Find the z value such that P(Z ≤ z) = 0.9082. A) z = 1.33 B) z = −1.33 C) z = 0.1814 D) z = 0.8186

A) z = 1.33

A random sample of size 100 is taken from a population described by the proportion p = 0.60. The probability that the sample proportion is greater than 0.62 is ______. A- 0.3415 B) ≈≈ 1 C- 0.4082 D- 0.6591

A)0.3415

Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that none of them has a degree in economics? A-0.343 B-0.900 C-0.300 D-0.027

A- 0.343

Consider the following discrete probability distribution. What is the probability that X is less than 5? A-0.35 B-0.15 C-0.10 D-0.45

A- 0.35

Which of the following can be represented by a continuous random variable? A- The time of a flight between Chicago and New York Correct B- The number of arrivals to a drive-through bank window in a four-hour period C- The score of a randomly selected student on a five-question multiple-choice quiz D- The number of defective light bulbs in a sample of five

A- The time of a flight between Chicago and New York

The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean ______ A- is closer to a normal distribution B- is closer to the standard deviation C- becomes smaller D-becomes larger

A- is closer to a normal distribution

The probability that a normal random variable is less than its mean is ______. A-0.5 B-Cannot be determined C-1.0 D-0.0

A-0.5

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the expected number of cars sold by the salesperson during a week? A-0.8 B-1.5 C-0 D-1

A-0.8

Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. The probability that the sample mean is between 25 and 30 school days is _______. A)0.8860 B)0.0228 C)0.0918 D)0.9082

A-0.8860

For any normally distributed random variable with mean μ and standard deviation σ, the proportion of the observations that fall outside the interval [μ − σ, μ + σ] is the closest to ______. A-0.3174 B-0.8413 C-0.0466 D-0.1687

A-03174

Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ______. A-50% chance that the actual return will be greater than 8% B-68% chance that the actual return will fall within −20% and 20% C-68% chance that the actual return will fall within 4% and 20% D-95% chance that the actual return will fall within −4% and 28%

A-50% chance that the actual return will be greater than 8%

Which of the following can be represented by a discrete random variable? A-The number of obtained spots when rolling a six-sided die B-The finishing time of participants in a cross-country meet C-The height of college students D-The average outside temperature taken every day for two weeks

A-The number of obtained spots when rolling a six-sided die

Which of the following is NOT a characteristic of the probability mass function of a discrete random variable X? A-The probability P(X ≤ x) for every possible value x is equal to 1. B-For every possible value x, the probability P(X = x) is between 0 and 1. C-The sum of probabilities P(X = x) over all possible values x is 1. D-Describes all possible values x with the associated probabilities P(X = x).

A-The probability P(X ≤ x) for every possible value x is equal to 1.

A consumer who is risk neutral is best characterized as ______________________________________________________. A-a consumer who completely ignores risk and makes his or her decisions based solely on expected values B- a consumer who underplays risk C-a consumer who demands a positive expected gain as compensation for taking risk D-a consumer who may accept a risky prospect even if the expected gain is negative

A-a consumer who completely ignores risk and makes his or her decisions based solely on expected values

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students that receive an A is 0.20 or less is ______. A-0.8900 B-0.1855 C-0.6266 D-0.8133

B) 0.1855

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students who receive an A is between 0.20 and 0.35 is A) 0.8133. B) 0.7776. C) 0.1867. D) 0.9633.

B) 0.7776.

Find the probability P(−1.96 ≤ Z ≤ 1.96). A) 0.0500 B) 0.9500 C) 0.9750 D) 1.9500

B) 0.9500

Find the z value such that P(−z ≤ Z ≤ z) = 0.922. A) z = −1.762 B) z = 1.762 C) z = −1.447 D) z = 1.447

B) z = 1.762

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. What is the probability that a class of 36 students will have an average greater than 70 on Professor Elderman's final exam? A- 0.6915 B- 0.9986 C- 0.0014 D- 0.3085

B- 0.9986

It is known that the length of a certain product X is normally distributed with μ = 26 inches. How is the probability P(X > 22) related to P(X < 22)? A-P(X>22) is the same as P(X<22). B-P(X>22) is greater than P(X<22). C-No comparison can be made with the given information. D-P(X>22) is smaller than P(X<22).

B- P(X>22) is greater than P(X<22).

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score is more than 230? A-0.9382 B-0.0620 C-0.3520 D-0.6480

B-0.0620

old miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find more than 16 ounces of gold in the next 1,000 tons of dirt excavated? A-0.5918 B-0.0912 C-0.4082 D-0.9082

B-0.0912

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians is less than $50,000? A-0.3707 B-0.2525 C-0.7486 D-0.6293

B-0.2525

Consider the following probability distribution. The standard deviation is _________. A-0.89 B-0.94 C-1.65 D-1.90

B-0.94

A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 16 inches. Suppose that 75 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean? A-3.41 B-1.85 C-4 D-16

B-1.85

It is known that 15% of the calculators shipped from a particular factory are defective. What is the probability that exactly four of ten chosen calculators are defective? A.) 0.4 B.) 0.04 C.) 0.99 D.) 0.01

B.) 0.04

The number of homes sold by a realtor during a month has the following probability distribution: What is the probability that the realtor sells no more than one house during a month? A.) 0.20 B.) 0.60 C.) 0.80 D.) 0.40

B.)0.60

The starting salary of an administrative assistant is normally distributed with a mean of $50,000 and a standard deviation of $2,500. We know that the probability of a randomly selected administrative assistant making a salary between μ − x and μ + x is 0.7416. Find the salary range referred to in this statement. A) $42,825 to $52,825 B) $42,825 to $57,175 C) $47,175 to $52,825 D) $47,175 to $57,175

C) $47,175 to $52,825

The probability P(Z < −1.28) is closest to ______. A) 0.20 B) −0.10 C) 0.10 D) 0.90

C) 0.10

A random sample of size 100 is taken from a population described by the proportion p = 0.60. The probability that the sample proportion is less than 0.55 is ______. A) 0.3669 B) 0.8461 C) 0.1537 D) ≈ 0

C) 0.1537

A random sample of size 100 is taken from a population described by the proportion p = 0.60. What are the expected value and the standard error for the sampling distribution of the sample proportion? A) 0.600 and 0.0024 B) 0.060 and 0.049 C) 0.600 and 0.049 D) 0.006 and 0.0024

C) 0.600 and 0.049

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228? A) 0.0618 B) 0.2390 C) 0.7600 D) 0.8212

C) 0.7600

You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. An inexpensive bag you are considering advertises to be good for temperatures down to 38°F. What is the probability that the bag will not be warm enough? A) 0.7500 B) 0.2266 C) 0.7734 D) 0.2734

C) 0.7734

The salary of teachers in a particular school district is normally distributed with a mean of $50,000 and a standard deviation of $2,500. Due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't? A) 45,100 B) 1.96 C) 54,900 D) −1.96

C) 54,900

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis? A) The tails get closer and closer to the x axis and eventually become this axis. B) The tails get closer and closer to the x axis and eventually cross this axis. C) The tails get closer and closer to the x axis but never touch it. D) The tails get closer and closer to the x axis and eventually touch it.

C) The tails get closer and closer to the x axis but never touch it.

Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is false about the z value corresponding to a given x value? A- A positive z = (x − μ)/σ indicates how many standard deviations x is above μ. B- A negative z = (x − μ)/σ indicates how many standard deviations x is below μ. C- The z value corresponding to a given value of x assumes any value between 0 and 1. D- The z value corresponding to x = μ is zero.

C- The z value corresponding to a given value of x assumes any value between 0 and 1.

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that, of a sample of 100 Indianapolis residents, at least 15% were rooting for the Patriots in Super Bowl XLVI? A-0.4763 B-0.9525 C-0.0478 D-0.0300

C-0.0478

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is greater than 18 is ______. A-0.4325 B-0.8413 C-0.1587 D-0.5675

C-0.1587

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is between 15 and 18 is ______. A-0.0228 B-0.8413 C-0.8186 D-0.8641

C-0.8186

On a particular production line, the likelihood that a light bulb is defective is 5% Ten light bulbs are randomly selected. Which is the probability that at most 3 light builds will be defective A-0.0115 B-0.9885 C-0.9990 D-0.0105

C-0.9990

According to a study by the centers for disease control and prevention, about 33% of U.S. births are Caesarean's deliveries, Suppose Seven expectant mothers are randomly selected. The expected number of mothers who will no have Caesarean delivery is ____. A-2.31 B-3.50 C-4.69 D-1.24

C-4.69

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. What is the probability that a class of 15 students will have a class average greater than 70 on Professor Elderman's final exam? A-0.0262 B-0.9738 C-Cannot be determined. D-0.6915

Cannot be determined.

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.0606. A) −1.55 B) 126 C) 1.55 D) 374

D) 374

The stock price of a particular asset has a mean and standard deviation of $58.50 and $8.25, respectively. Use the normal distribution to compute the 95th percentile of this stock price. A-44.93 B-1.645 C) −1.645 D) 72.07

D) 72.07

If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population? A) For a sample size n < 50, the sampling distribution of the sample mean is normally distributed. B) For a sample size n > 30, the sampling distribution of the sample mean is normally distributed. C) For a sample size n < 30, the sampling distribution of the sample mean is normally distributed. D) For any sample size n, the sampling distribution of the sample mean is normally distributed.

D) For any sample size n, the sampling distribution of the sample mean is normally distributed.

et X be normally distributed with mean µ = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736. A)20.30 B)0.94 C)−0.94 D)29.70

D)29.70

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians exceeds $60,000? 0.6915 0.3085 0.8413 0.1587

D- 0.1587

Bias can occur in sampling. Bias refers to ______. A- the use of cluster sampling instead of stratified random sampling B- the division of the population into overlapping groups C- the creation of strata, which are proportional to the stratum's size D- the tendency of a sample statistic to systematically over- or underestimate a population parameter

D- the tendency of a sample statistic to systematically over- or underestimate a population parameter

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car. A-0.5000 B-0.2420 C-0.7580 D-0.0000

D-0.0000

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that from a sample of 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLVI? A-0.9908 B- 0.4954 C-0.0212 D-0.0092

D-0.0092

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots.What is the probability that from a sample of 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLVI? A-0.9908 B-0.4954 C-0.0212 D-0.0092

D-0.0092

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take more than five hours to construct a soapbox derby car A-0.4772 B-0 C-0.9772 D-0.0228

D-0.0228

Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours. What is the probability that the battery will last more than 9 hours before running out of power? A-0.4525 B-1.6667 C-0.9525 D-0.0478

D-0.0478

For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed $10-off coupons. What is the probability that no more than one of the customers redeems the coupon? A-0.3513 B-0.4015 C-0.2472 D-0.7528

D-0.7528

You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. One sleeping bag you are considering advertises that it is good for temperatures down to 25°F. What is the probability that this bag will be warm enough on a randomly selected May night at the park? A-0.8800 B-0.3106 C-0.1894 D-0.8092

D-0.8092

It is known that 15% of the calculators shipped from a particular factory are defective. What is the probability that exactly four of ten chosen calculators are defective? A.) The circumference of a randomly generated circle B.)The average distance achieved in a series of long jumps C. )The time of a flight between Chicago and New York D.)The number of defective light bulbs in a sample of five

D.) The number of defective light bulbs in a sample of five

Consider the following probability distribution. The expected value is _____. A.) 0.1 B.) −1.0 C.) 1.0 D.) −0.1

D.) −0.1

A standard normal variable Z can be transformed to the normally distributed random variable X with only mean µ known. TRUE OR FALSE

FALSE

We are often interested in finding the probability that a continuous random variable assumes a particular value. TRUE OR FALSE

FALSE

A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations. TRUE OR FALSE

TRUE

The probability density function of a continuous random variable is the counterpart to the probability mass function of a discrete random variable. TRUE OR FALSE

TRUE

How would you characterize a consumer who is risk loving?

a consumer who may accept a risky prospect even if the expected negative.

which of the following statements is the most accurate about a binomial random variable?

it counts the number of successes in a given number of trials