Review #2

Scores on a business statistics final exam are normally distributed with a mean of 74 and standard deviation of 8. The z value for the exam score of 84 equals ______.

(84-74)/8

The probability P(Z < −1.28) is closest to ______.

.10

Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced.Given that a respondent read a book in the last month, the probability that he or she is at least 30 years old is the closest to ________

.46 (CLOSEST TO)

The probability that a normal random variable is less than its mean is ______.

.5

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers biking given that he or she is 35 years old or older.

35+ biking total / over 35 total (GIVEN)

Find the missing values marked xx and yay in the following contingency table

353-132-131 = 90 yy 146-65-61 = 20 xx

What is probability?

A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence

A sample space contains _________.

All possible outcomes of an experiment

Mutually exclusive events ___________.

Do not share common outcomes

A discrete random variable X assumes an infinite and uncountable number of distinct values.

False

The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual who is a female or prefers science?

Female total + male science

Susan has been on a bowling team for 16 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 236, with a standard deviation of 14. Using an appropriate normal transformation, what is the probability that in a one-game playoff, her score is more than 242?

P( X > 242) = P( Z > 0.43) = 1 − P(Z ≤ 0.43) = 1.0 − 0.6664 = 0.3336.

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers running.

Running total / TOTAL

An analyst estimates that the year-end price of a stock has the following probabilities: The stock's expected price at the end of the year is _______.

Stock price x Probability

An analyst believes the probability that US stock returns exceed long-term corporate bond returns over a five-year period is based on personal assessment.

Subjective probability

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.

The 95th percentile is the x value, where P(X ≤ x) = 0.95. Then, P(Z ≤ (x − 58.5) / 8.25) = 0.95, which implies that (x − 58.5) / 8.25 = 1.645. Therefore, x = 72.07.Alternatively, the appropriate Excel function is =NORM.INV(0.95,58.5,8.25) = 72.07.

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?

The appropriate Excel function is =1-NORM.DIST(60000,54000,12000/SQRT(4),TRUE) = 0.1587.

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, use an appropriate normal transformation to calculate the probability that her average score is more than 230.

The appropriate Excel function is =1−NORMDIST(230,225,13/SQRT(16),TRUE) = 0.0620.

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?

The appropriate Excel function is =SQRT(0.6*(1 − 0.6)/100) = 0.049.

A random sample of size 36 is taken from a population with mean µ = 22 and standard deviation σ = 6. What are the expected value and the standard deviation for the sampling distribution of the sample mean?

The mean and standard error of the sample mean are calculated as E(X¯¯¯)=μ��¯=� = 22 and se(X¯¯¯)=σn√���¯=�� = 6 / 6 = 1.00.

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 approximately ______.

The normal distribution is symmetric around its mean: P(X < μ) = P(X > μ) = 0.5.

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 between 2.5 and 3.5 hours to construct a soapbox derby car.

The normal transformation z=x−μσ�=�−�� implies that P(2.5 ≤ X ≤ 3.5) = (−0.50 ≤ Z ≤ 0.50) = P(Z ≤ 0.50) − P(Z ≤ −0.50) = 0.6915 − 0.3085 = 0.3830.The appropriate Excel function is =NORM.DIST(3.5,3,1,TRUE) − NORM.DIST(2.5,3,1,TRUE) = 0.3830.

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.

The normal transformation z=x−μσ�=�−�� implies that P(X > 5) = P(Z > 2) = 1 − P(Z ≤ 2) = 1 − 0.9772 = 0.0228.The appropriate Excel function is =1 − NORM.DIST(5,3,1,TRUE) = 0.0228.

Which of the following can be represented by a discrete random variable?

The number of defective light bulbs in a sample of twenty

Which of the following can be represented by a continuous random variable?

The time of a flight between Chicago and New York

Find the probability P(−1.96 ≤ Z ≤ 0).

The z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Compute P(−1.96 ≤ Z ≤0) as P(Z ≤ 0) − P(Z ≤ −1.96) = 0.50 − 0.025 = 0.475.

A six-sided, unfair (weighted) die has the following probability distribution. Find the probability of rolling a 3 or less.

Total probability of 1-3

A Poisson random variable counts the number of successes (occurrences) of a certain event over a given interval of time or space.

True

A binomial random variable is defined as the number of successes achieved in the n trials of a Bernoulli process.

True

A continuous random variable X assumes an infinite and uncountable number of distinct values.

True

A risk-averse consumer may decline a risky prospect even if it offers a positive expected value.

True

A risk-neutral consumer ignores risk and makes his or her decisions solely on the basis of expected value.

True

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. Group startsTrue or False

True

Bias refers to the tendency of a sample statistic to systematically overestimate or underestimate a population parameter.

True

Consider the following two events. A = The survey respondent is less than 40 years old, B = The survey respondent is 40 years or older. Events A and B are mutually exclusive and exhaustive

True

For any population proportion p, the sampling distribution of P¯¯¯�¯ will be approximately normal if the sample size n is sufficiently large. As a general guideline, the normal distribution approximation is justified when np ≥ 5 and n(1 −p) ≥ 5.

True

In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. Then simple random samples are drawn from each stratum, which are proportional to the stratum's size in the population.

True

Mutually exclusive and collectively exhaustive events contain all outcomes of a sample space, and they do not share any common outcomes

True

Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.

True

Social-desirability bias refers to systematic difference between a group's 'socially acceptable" responses to a survey or poll and this group's ultimate choice.

True

The intersection of two events A and B, denoted by A (n) B, is the event consisting of all outcomes that are in A and B

True

The normal probability distribution is symmetric and bell-shaped.

True

The standard deviation of X¯¯¯�¯ (standard error of the sample mean) equals the population standard deviation divided by the square root of the sample size.

True

The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation (or variance) equal to one.

True

The standard normal table is also referred to as the z table.

True

Two events A and B are independent if the occurrence of one of them does not influence the probability of the occurrence of the other event.

True

When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate.

True

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers running and is under 35 years of age.

Under 35 running total/TOTAL

Find the z value such that P(−z ≤ Z ≤ z) = 0.95.

Use the z table with cumulative probability P(Z ≤ z) = 0.95 + 0.025 = 0.975 to find z = 1.96.

Find the z value such that P(Z ≤ z) = 0.9082.

Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z.

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.9394.

Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Given that P(X ≤ x) = 0.9394 implies that (x − 250) / 80 = 1.55, hence x = 374.The appropriate Excel function is =NORM.INV(0.9394,250,80) = 374.

Let X be normally distributed with mean µ = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736.

Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Given that P(X ≥ x) = 0.1736 implies that P(X ≤ x) = 1 − 0.1736 = 0.8264. Then, (x − 25) / 5 = 0.94; hence x = 29.7.The appropriate Excel function is =NORM.INV(1 − 0.1736,25,5) = 29.70.

Suppose that, on average, electricians earn approximately µ = $54,100 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $13,000. Given a sample of four electricians, what is the standard deviation for the sampling distribution of the sample mean?

calculated as se(X¯¯¯)=σn√���¯=�� = $13,000 / 2 = $6,500.``

Consider the following discrete probability distribution. What is the probability that X is greater than 0?

everything above zero

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the probability that the salesperson will sell one car during a week?

frequency/TOTAL weeks

For qualitative data, the most appropriate control chart to monitor the proportion of a certain characteristic in a production process is a(n)

p chart

In any production process, variations in the quality of the end product are inevitable. Assignable variation refers to ______.

specific events or factors that can usually be identified and eliminated

An analyst believes that a stock's return depends on the state of the economy, for which she has estimated the following probabilities: According to the analyst's estimates, the expected return of the stock is ____.

sum of all Probability x Return

According to the central limit theorem, for any population, the sampling distribution of the sample mean X¯¯¯�¯ is approximately normal if ______.

the sample size n ≥ 30

For quantitative data, the most appropriate control chart to monitor central tendency in a production process is a(n)

x chart

The union of events A = {apple pie, peach pie, pumpkin pie} and B = {cherry pie, blueberry pie, pumpkin pie} is ___________.

{apple pie, peach pie, pumpkin pie, cherry pie, blueberry pie}

The intersection of events A = {apple pie, peach pie, pumpkin pie} and B = {cherry pie, blueberry pie, pumpkin pie} is ________________

{pumpkin pie}

The ______ of the sample mean X¯¯¯�¯ is the same as the population mean.

μ