Exam 2 BADM 275
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 mean of a standard normal probability distribution _____.
None of the answers is correct.
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.
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
Let R, which is a normally distributed random variable with mean 0.01 and standard deviation 0.04, denote the return on a certain companys portfolio next month(0.01, 0.04 raised to the 2nd power). What are the minimum and maximum of the middle 95% of the return?
+2 and -2 standard deviations from the mean equals the middle 95% of the return 0.01 +2(0.04) and 0.01 - 2(0.04) equal the middle 95%. 0.01+0.08=0.09 0.01-0.08= -0.07 So the minimum and maximum values of the middles 95% of the return are -0.07 and 0.09
Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the relative frequency method for computing probability is used, the probability that the next customer will purchase a computer is _____.
.25
There is a 60% chance of getting stuck in traffic when leaving the city. On two separate days, what is the probability that you get stuck in traffic both days?
.36
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
A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl?
.875
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 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
Let R, which is a normally distributed random variable with mean 0.01 and standard deviation 0.04, denote the return on a certain companys portfolio next month(0.01, 0.04 raised to the 2nd power). What is the probability of getting a negative return?
0.4013
Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table. The probability that a consumer purchases an extended warranty given that he/she has purchased a digital camera is
0.42
The area that lies between 0 and 3.01
0.4987
Let R, which is a normally distributed random variable with mean 0.01 and standard deviation 0.04, denote the return on a certain companys portfolio next month(0.01, 0.04 raised to the 2nd power). What is the probability of a return less than 0.05?
0.8413
if a student is chosen at random, find the probability of getting someone who is a man or a non-drinker.
0.930
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 quiz consists of 100 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers?
5
High temperatures in a certain city for the month of august follow a uniform distribution over the interval 61 degrees F to 91 degrees F. Find the high temperature which 90% of the august days exceed. (uniform distribution)
64 degrees F
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%
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.
Factory Omaha: p=0.25 q=0.75 Probability that the pair of shoes are mislabeled and from Omaha: 0.25*0.01=0.0025 Factory Chicago: p=0.30 q=0.70 Probability that the pair of shoes are mislabeled and from Chicago: 0.30*0.005=0.0015 Factory Seattle: p=0.45 q=0.55 Probability that the pair of shoes are mislabeled and from Seattle: 0.45*0.02=0.0090 Combined Probability that the pair of shoes are mislabeled: 0.0025+0.0015+0.0090=0.0130=0.013
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 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.
What statement is always true?
P(A)+ = 1 - P(A sub c)
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(M2|U)= (0.4*0.25) / [ (0.6*0.1) + (0.4*0.25)] = 0.1 / (.06+.1) = 0.625
Classify the statement as an example of classical probability or subjective probability. The probability that cab fares will rise during the winter is 0.05.
Subjective probability
Which of the following is NOT a characteristic of the normal probability distribution?
The graph of the curve is the shape of a rectangle.
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) 10.0*.3+10.2*.3+10.6*.1=3+3.06+1.06=7.12 b) (9.5*.1)+(9.8*.2)+(10.0*.3)+(10.2*.3)+(10.6*.1)=10.03 c)9.025+19.208+30+31.212+11.236=100.681 [x²*p(x)]-10.03^2 100.681-10.03^2=0.0801
In a random sample of UTC students, 50% indicated they are Business majors, 40% Engineering majors, and 10% Other majors. Of the Business majors, 60% were females; whereas 30% of Engineering majors were females. Finally, 20% of the Other majors were female. a. What percentage of students in this sample was female? b. Given that a person is female, what is the probability that she is an engineering major?
a. The percentage of students that are female= (0.5*0.6) + (0.4*0.3) + (0.1*0.2) = 0.3 + 0.12 + 0.02 = 0.44 b. P(Engineer | female)= [P(engineering major) * P(female | engineer)] / P(female) = (0.4*0.3) / 0.44 = 0.278
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.
a. .25/.4= 0.625 b. .72 + .25 - .4 = 0.57 c. No intersection. No because P(raise and promotion) = 0.25. If it equaled 0, then it would be mutually exclusive d. no because the values are not equal to each other. P(Raise|promoted) and P(raise)
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) = .6P(stock goes up 20% | level GDP) = .5P(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 will go up) = .6*.3+.5*.3+.4*.4 = .49 b. P (rise or fall) = exclude the middle 'level gdp'... = (.6*.3+.4*.4)/.49 = .6939 c. p ( stock and level goes down 20% ) = .5*.3 / p (stock goes down 20%) p (stock goes down 20%)= .6*.4+.3*.5+.4*.3 = .51 p ( stock and level goes down 20% )=.5*.3/.51 = .294
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. P(X=0)=12C0x0.550x0.4512-0=0.4512=0.0001 b. P(x=12)=12C 12x(0.55)12x(0.45)0=0.5512=0.0008 c. P(x=4)=12C^4x0.55^4x0.45^8 d. P(x=3)=P(0)+P(1)+P(2)=(12C0x0.550x0.4512)+(12C2x0.552x0.4510)+(0.0068)=0.0078 e. E(X)=np=12x0.55=6.6 V(x)=npq=12x0.55x0.45=2.97
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.) mean= (0*.05)+(1*.10)+(2*.15)+(3*.20)+(4*.15)+(5*.10)+(6*.10)+(7*.05)+(8*.05)+(9*.05)= answer= 3.9 b.)SD= sqrt((0^2*.05)+(1^2*.10)+(2^2*.15)+(3^2*.20)+(4^2*.15)+(5^2*.10)+(6^2*.10)+(7^2*.05)+(8^2*.05)+(9^2*.05)- (3.9)^2)= answer= 2.34 c.) 3.9+(2*2.34)= answer= 8.58 = 9
A continuous random variable may assume _____.
all values in an interval or collection of intervals
The ___ probability of an outcome is obtained by dividing the number of ways an event can occur by the number of possible outcomes.
classical
the number of bottles of juice sold in a cafeteria during lunch
discrete
the number of emails received on any given day
discrete
the sum of the probabilities of a discrete probability distrubution must be
equal to one
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
You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common.
mutually exclusive events
The expected value of a random variable is the _____.
mean value
According to government data, the probability that an adult was never in a museum is 10%. In a random survey of 20 adults, what is the mean and standard deviation of the number that were never in a museum?
mean: 2; standard deviation: 1.34164079
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
The probability of the intersection of two mutually exclusive events _____.
must always be equal to 0
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