Mastery 5
hotjpka69
mastery_5.odt1.
Customers make purchases at a convenience store, on average, every fourteen minutes. It is fair to assume that the time between customer purchases is exponentially distributed. Jack operates the cash register at this store.
a-1. What is the rate parameter λ? (Round your answer to 4 decimal places.)
Rate parameter λ
a-2. What is the standard deviation of this distribution? (Round your answer to 1 decimal place.)
Standard deviation
b.
Jack wants to take a ten-minute break. He believes that if he goes right after he has serviced a customer, he will lower the probability of someone showing up during his ten-minute break. Is he right in this belief?
Yes
No
c.
What is the probability that a customer will show up in less than ten minutes? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)
Probability
d.
What is the probability that nobody shows up for over fourty-five minutes? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)
Probability
rev: 08_01_2013_QC_33082
2.
Suppose that the average IQ score is normally distributed with a mean of 120 and a standard deviation of 18. In addition to providing the answer, state the relevant Excel commands. (Use Excel)
a.
What is the probability a randomly selected person will have an IQ score of less than 90? (Round your answer to 4 decimal places.)
Probability
b.
What is the probability that a randomly selected person will have an IQ score greater than 130? (Round your answer to 4 decimal places.)
Probability
c.
What minimum IQ score does a person have to achieve to be in the top 1.8% of IQ scores? (Round your answer to 2 decimal places.)
Minimum IQ score
rev: 08_01_2013_QC_33082
3.
The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 25 minutes and 4 minutes, respectively. Use Table 1.
a.
Find the probability that a randomly picked assembly takes between 22 and 27 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Probability
b.
It is unusual for the assembly time to be above 35 minutes or below 15 minutes. What proportion of assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Proportion of assembly times
rev: 08_01_2013_QC_33082, 11_01_2013_QC_37833
4.
A random variable X is exponentially distributed with a mean of 0.16.
a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.)
Rate parameter λ
a-2. What is the standard deviation of X? (Round your answer to 3 decimal places.)
Standard deviation X
b. Compute P(X > 0.24). (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)
P(X > 0.24)
c. Compute P(0.09 ≤ X ≤ 0.24). (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)
P(0.09 ≤ X ≤ 0.24)
rev: 08_01_2013_QC_33082
5.
Entrance to a prestigious MBA program in India is determined by a national test where only the top 10% of the examinees are admitted to the program. Suppose it is known that the scores on this test are normally distributed with a mean of 450 and a standard deviation of 90. Parul Monga is trying desperately to get into this program. What is the minimum score that she must earn to get admitted? Use Table 1. (Round "z" value to 2 decimal places and final answer to 1 decimal place.)
Minimum score
rev: 08_01_2013_QC_33082
6.
The mileage (in 1000s of miles) that car owners get with a certain kind of radial tire is a random variable having an exponential distribution with a mean of 52. In addition to providing the answer, state the relevant Excel commands. (Use Excel)
a.
What is the probability that a tire will last at most 44,000 miles? (Round your answer to 4 decimal places.)
Probability
b.
What is the probability that a tire will last at least 66,000 miles? (Round all intermediate calculations and your final answer to 4 decimal places.)
Probability
c.
What is the probability that a tire will last between 76,000 and 79,000 miles? (Round all intermediate calculations and your final answer to 4 decimal places.)
Probability
rev: 08_01_2013_QC_33082, 03_10_2014_QC_46226
7.
A random variable X follows the uniform distribution with a lower limit of 720 and an upper limit of 920.
a.
Calculate the mean and the standard deviation of this distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.)
Mean
Standard deviation
b.
What is the probability that X is less than 870? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Probability
rev: 08_01_2013_QC_33082
8.
The historical returns on a balanced portfolio have had an average return of 7% and a standard deviation of 18%. Assume that returns on this portfolio follow a normal distribution. Use the empirical rule for normal distributions to answer the following questions.
a. What percentage of returns were greater than 43%? (Round your answer to 1 decimal place.)
Percentage of returns %
b. What percentage of returns were below −47%? (Round your answer to 1 decimal place.)
Percentage of returns %
rev: 08_01_2013_QC_33082
9.
The random variable X is normally distributed. Also, it is known that P(X > 187) = 0.09. Use Table 1.
a.
Find the population mean μ, if the population standard deviation σ = 18. (Round "z" value to 2 decimal places and final answer to 1 decimal place.)
Mean
b.
Find the population mean μ, if the population standard deviation σ = 30. (Round "z" value to 2 decimal places and final answer to 1 decimal place.)
Mean
c.
Find the population standard deviation σ, if the population mean μ = 164. (Round “z” value to 2 decimal places, and final answer to 2 decimal places.)
Standard deviation
d.
Find the population standard deviation σ, if the population mean μ = 156. (Round “z” value to 2 decimal places, and final answer to 2 decimal places.)
Standard deviation
rev: 08_01_2013_QC_33082
10.
On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeders. Assume the time that elapses between successive speeders is exponentially distributed with a mean of 23 minutes.
a. Calculate the rate parameter λ. (Round your answer to 4 decimal places.)
Rate parameter λ
b.
What is the probability of a waiting time less than 12 minutes between successive speeders? (Round your answer to 4 decimal places.)
Probability
c.
What is the probability of a waiting time in excess of 32 minutes between successive speeders? (Round your answer to 4 decimal places.)
Probability
rev: 08_01_2013_QC_33082
11.
The scheduled arrival time for a daily flight from Boston to New York is 9:30 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:05 am and a late arrival time of 9:55 am.
a.
After converting the time data to a minute scale, calculate the mean and the standard deviation for the distribution. (Round your answers to 2 decimal places.)
Mean minutes
Standard deviation minutes
b.
What is the probability that a flight arrives late (later than 9:30 am)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Probability
rev: 08_01_2013_QC_33082
12.
A construction company in Naples, Florida, is struggling to sell condominiums. In order to attract buyers, the company has made numerous price reductions and better financing offers. Although condominiums were once listed for $300,000, the company believes that it will be able to get an average sale price of $229,000. Let the price of these condominiums in the next quarter be normally distributed with a standard deviation of $14,000. Use Table 1.
a.
What is the probability that the condominium will sell at a price (i) Below $205,000?, (ii) Above $254,000? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Probability
Below $205,000
Above $254,000
b.
The company is also trying to sell an artist’s condo. Potential buyers will find the unusual features of this condo either pleasing or objectionable. The manager expects the average sale price of this condo to be the same as others at $229,000, but with a higher standard deviation of $17,000. What is the probability that this condo will sell at a price (i) Below $205,000?, (ii) Above $254,000? (Round your answers to 4 decimal places.)
Probability
Below $205,000
Above $254,000
rev: 08_01_2013_QC_33082
13.
When crossing the Golden Gate Bridge, traveling into San Francisco, all drivers must pay a toll. Suppose the amount of time (in minutes) drivers wait in line to pay the toll follows an exponential distribution with a probability density function of f(x) = 0.29e−.29x.
a.
What is the mean waiting time that drivers face when entering San Francisco via the Golden Gate Bridge? (Round your answer to 2 decimal places.)
Mean waiting time
b.
What is the probability that a driver spends more than the average time to pay the toll? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)
Probability
c.
What is the probability that a driver spends more than 13 minutes to pay the toll? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)
Probability
d.
What is the probability that a driver spends between 6 and 10 minutes to pay the toll? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)
Probability
rev: 08_01_2013_QC_33082
14.
Lisa Mendes and Brad Lee work in the sales department of an AT&T Wireless Store. Lisa has been signing in an average of 69 new cell phone customers every month with a standard deviation of 26, while Brad signs in an average of 75 new customers with a standard deviation of 17. The store manager offers both Lisa and Brad a $100 incentive bonus if they can sign in more than 100 new customers in a month. Assume a normal distribution to answer the following questions. Use Table 1.
a.
What is the probability that Lisa will earn the $100 incentive bonus? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Probability
b.
What is the probability that Brad will earn the $100 incentive bonus? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Probability
rev: 08_01_2013_QC_33082.
15.
The average rent in a city is $1,590 per month with a standard deviation of $260. Assume rent follows the normal distribution. Use the empirical rule for normal distributions to answer the following questions.
a.
What percentage of rents are between $1,070 and $2,110? (Round your answer to the nearest whole percent.)
Percentage of rents %
b.
What percentage of rents are less than $1,070? (Round your answer to 1 decimal place.)
Percentage of rents %
c. What percentage of rents are greater than $2,370?(Round your answer to 1 decimal place.)
Percentage of rents %
rev: 08_01_2013_QC_33082, 11_14_2013_QC_
