BADM 275 - Exam 2 Study Guide

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 360 hours and a standard deviation of 5 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation of the mean?

68%

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The expected assembly time (in minutes) is

8

Twenty percent of people at a company picnic got food poisoning. What percent of the people at the picnic did NOT get food poisoning?

80%

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The standard deviation of assembly time (in minutes) is approximately _____.

None of the answers is correct.

The mean of a standard normal probability distribution _____.

None of the answers is correct.

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What percent of players weigh between 180 and 220 pounds?

None of the answers is correct.

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What percent of players weigh between 180 and 220 pounds?

The area under the standard normal curve to the left of z = 0 is negative.

A description of how the probabilities are distributed over the values the random variable can assume is called a(n) _____.

probability distribution

For a standard normal distribution, the probability of obtaining a z value between -1.9 and 1.7 is _____.

.9267

If A and B are independent events with P(A) = .4 and P(B) = .25, then P(A∪B) = _____.

.55

If A and B are independent events with P(A) = .2 and P(B) = .6, then P(A∪B) = _____.

.68

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in 7 minutes or more is _____.

.75

The probability of at least one head in two flips of a coin is _____.

.75

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in less than 6 minutes is _____.

0

The range of probability is _____,

0 to 1, inclusive

The probability that a house in an urban area will develop a leak is 6%. If 87 houses are randomly selected, what is the probability that none of the houses will develop a leak?

0.005

The weekly salaries of elementary school teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected elementary school teacher earns more than $525 a week?

0.2177

The area that lies between -1.10 and -0.36

0.2237

According to insurance records a car with a certain protection system will be recovered 91% of the time. Find the probability that 5 of 6 stolen cars will be recovered.

0.337

The area that lies between 0 and 3.01

0.4987

The probability that a house in an urban area will develop a leak is 5%. If 20 houses are randomly selected, what is the mean of the number of houses that developed leaks?

1

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1401?

1.08

A company manufactures shoes in three different factories. Factory Omaha Produces 25% of the company's shoes, Factory Chicago produces 30%, and factory Seattle produces 45%. One percent of the shoes produced in Omaha are mislabeled, 0.5 % of the Chicago shoes are mislabeled, and 2% of the Seattle shoes are mislabeled. If you purchase one pair of shoes manufactured by this company what is the probability that the shoes are mislabeled? Round to the nearest thousandth.

P(0.5% of 30%) = (0.5/100) x (30/100) = 0.3 x 0.005 = 0.0015 Seattle produces 45% of shoes ; mislabeled shoes 2% P(2% of 45%) = (2/100) x (45/100) = 0.45*0.02 = 0.009 Probability of mislabeled = P(1% of 25%) + P(0.5% of 30%) + P(2% of 45%) = 0.0025 + 0.0015 +0.009 = 0.0013 Probability of mislabeled = 0.001

Ambell Company uses batteries from two different manufacturers. Historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours. Only 75% of the batteries from manufacturer 2 last for over 40 hours. A battery in a critical tool fails at 32 hours. What is the probability it was from manufacturer 2?

P(<40 hrs) = P(m1 and <40 hrs) + P(m2 and <40 hrs) = 60/100 x (1 - 90/100) + 40/100 x (1 - 75/100) = 16/100 P(A given B) = P(A and B) / P(B) P(m2 given <40 hrs) = P(m2 and <40hrs) / P(<40hrs) = (40/100 x (1 - 75/100)) / (16/100) = (10/100) / (16/100) = 5/8 = 0.625 or 62.5%

Which of the following statements is always true?

P(A) = 1 −P(Ac)

As a company manager for Claimstat Corporation there is a .40 probability that you will be promoted this year. There is a .72 probability that you will get a promotion or a raise. The probability of getting a promotion and a raise is .25. a.If you get a promotion, what is the probability that you will also get a raise? b.What is the probability of getting a raise? c.Are getting a raise and being promoted independent events? Explain using probabilities. d.Are these two events mutually exclusive? Explain using probabilities.

P(promotion) = 0.40 P(promotion or raise) = 0.72 a. P(raise/promotion) = 0.25/0.40 = 0.625 b. 0.72 = 0.40 + P(raise) - 0.25 0.72 = 0.15 + P(raise) P(raise) = 0.72 - 0.15 P(raise) = 0.57 c. (0.40) (0.57) = 0.228 d. The two events are mutually exclusive if: P(promotion and raise) = 0 But, P(promotion and raise) = 0.25 so, the events are not mutually exclusive.

Which of the following is NOT a characteristic of the normal probability distribution?

The random variable assumes a value within plus or minus three standard deviations of its mean 99.72% of the time.

Which of the below is not a requirement for binomial experiment?

The trials are mutually exclusive.

Which of the following statements about a discrete random variable and its probability distribution is true?

Values of f(x) must be greater than or equal to zero.

The uniform probability distribution is used with _____.

a continuous random variable

The weight of an object, measured in grams, is an example of _____.

a continuous random variable

The weight of an object, measured to the nearest gram, is an example of _____.

a discrete random variable

The probability distribution for the rate of return on an investment is Rate of Return (%) Probability 9.5 .1 9.8 .2 10.0 .3 10.2 .3 10.6 .1 ​ a.What is the probability that the rate of return will be at least 10%?b.What is the expected rate of return? c.What is the variance of the rate of return?

a) P(the rate of return will be at least 10%)= P(return = 10.0) + P(return=10.2) +P(return= 0.6) 0.3 + 0.3+0.1 = 0.7 b) Expected return = 9.5*0.1 + 9.8*0.2 + 10.0*0.3 + 10.2*0.3 + 10.6*0.1 = 10.03 c) Variance = ((9.5-10.03)^2)*0.1 + ((9.8-10.03)^2)*0.2 + ((10.0-10.03)^2)*0.3 + ((10.2-10.03)^2)*0.3 + ((10.6-10.03)^2)*0.1 = 0.0801

A continuous random variable may assume

all values in an interval or collection of intervals

The symbol ∩ shows the _____.

intersection of events

The expected value of a discrete random variable _____.

is the average value for the random variable over many repeats of the experiment

The expected value of a random variable is the _____.

mean value

A recent survey found that 79% of all adults over 50 wear sunglasses for driving. In a random sample of 80 adults over 50, what is the mean and standard deviation of those that wear sunglasses?

mean: 63.2; standard deviation: 3.64307562

A numerical description of the outcome of an experiment is called a _____.

random variable

The variance is a weighted average of the _____.

squared deviations from the mean

Bayes' theorem is used to compute _____.

the posterior probabilities

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is _____.

the same for each interval

The addition law is potentially helpful when we are interested in computing the probability of _____.

the union of two events

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable follows a(n) _____ distribution.

uniform

The symbol ∪ indicates the _____.

union of events

Which of the following is NOT a required condition for a discrete probability function?

∑f(x) = 0

Three applications for admission to a local university are checked to determine whether each applicant is male or female. The number of sample points in this experiment is _____.

8

A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day. The distribution is as follows: Number sold in a day 0 5 10 15 20 Prob(Number sold) 0.22 0.24 0.13 0.25 0.16 Find the number of cheesecakes that this local bakery expects to sell in a day.

9.45

Which of the following is not true about the standard normal distribution?

The area under the standard normal curve to the left of z = 0 is negative.

An investment advisor recommends the purchase of shares in Infogenics, Inc. He has made the following predictions: P(stock goes up 20% | rise in GDP) = .6 P(stock goes up 20% | level GDP) = .5 P(stock goes up 20% | fall in GDP) = .4 An economist has predicted that the probability of a rise in the GDP is 30%, whereas the probability of a fall in the GDP is 40%. a. What is the probability that the stock will go up 20%? b. We have been informed that the stock has gone up 20%. What is the probability of a rise or fall in the GDP? c. We have been informed that the stock has gone down 20%. What is the probability of a level in the GDP?

a. P(Stock goes up by 20%) = P(A) = (0.6 x 0.3) + (0.5 x 0.3) + (0.4 x 0.4) = 0.49 b. Prob. of a rise or fall in GDP = (0.6 x 0.3) / 0.49 + (0.5 x 0.3) / 0.49 = 0.33 / 0.49 = 0.763469 c. Prob. of a level in GDP = (1 - 0.5) x 0.3 / 1 - 0.49 = 0.15 / 0.51 = 5/17 = 0.2941176

The salespeople at Gold Key Realty sell up to 9 houses per month. The probability distribution of a salesperson selling x houses in a month is as follows: Sales (x) 0 1 2 3 4 5 6 7 8 9 Probability f (x) .05 .10 .15 .20 .15 .10 .10 .05 .05 .05 a. What is the mean for the number of houses sold by a salesperson per month? b. What is the standard deviation for the number of houses sold by a salesperson per month? c. Any salesperson selling more houses than the amount equal to the mean plus two standard deviations receives a bonus. How many houses per month must a salesperson sell to receive a bonus?

a. The mean for the number of houses sold = 3.90 b. The standard deviation for the number of houses sold = 2.34 c. Since the mean plus two standard deviations is 9.39, the number of houses per month that needs to be sold for the salesperson to receive a bonus must be more than 9 houses.

Fifty-five percent of the applications received for a credit card are accepted. Among the next 12 applications, a.what is the probability that all will be rejected? b.what is the probability that all will be accepted? c.what is the probability that exactly 4 will be accepted? d.what is the probability that fewer than 3 will be accepted?e.Determine the expected number and the variance of the accepted applications.

a. The probability that all applications will be rejected is 0.0001. b. The probability that all applications will be accepted is 0.0008. c. The probability that exactly 4 applications will be accepted is approximately 0.0762. d. The probability that fewer than 3 applications will be accepted is approximately 0.0078. e. The mean and variance of the accepted application is 6.6 and 2.97.

A government agency has 6,000 employees. The employees were asked whether they preferred a four-day work week (10 hours per day), a five-day work week (8 hours per day), or flexible hours. You are given information on the employees' responses broken down by gender. Male Female Total Four days 300 600 900 Five days 1,200 1,500 2,700 Flexible 300 2,100 2,400 Total 1,800 4,200 6,000 ​ a.What is the probability that a randomly selected employee is a man and is in favor of a four-day work week? b.What is the probability that a randomly selected employee is female? c.A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours. d.What percentage of employees is in favor of a five-day work week?e.Given that a person is in favor of flexible time, what is the probability that the person is female? f.What percentage of employees is male and in favor of a five-day work week

a. 300 / 6000 = 0.05 b. 4200 / 6000 = 0.7 c. (2100 / 6000) / (4200 / 6000) = 0.5 d. 2700 / 6000 = 0.45 e. (2100 / 6000) / (2400 / 6000) = 0.875 f. 1200 / 6000 = 0.2