Brad Smith has done some analysis about the profitability of the bicycle shop. If Brad builds the large bicycle shop, he will earn $60,000 if the market is favorable, but he will lose $40,000 if the market is unfavorable. The small shop will return a $30,000 profit in a favorable market and a $10,000 loss in an unfavorable market. At the present time, he believes that there is a 50-50 chance that the market will be favorable. His former marketing professor will charge him $5,000 for the marketing research. Furthermore, there is a 0.9 probability that the market will be favorable given a favorable outcome from the study.
What is the highest Expected Monetary Value for Brad’s decision?
In: Statistics and Probability
Arthur is choosing whether to buy insurance against the risk of theft of car. He has savings of $64,000. His utility function over income x is u(x) = x1/3. If his car is stolen and he does not have insurance, he will need to pay $9128 for another car. A company offers full insurance that will pay out $9128 if the car is stolen. What is the highest price Arthur will be willing to pay for the insurance (round to the nearest dollars) if the probability of having his car stolen is 0.1?
Group of answer choices
$2837
$1019
$1300
$955
In: Economics
10. A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.
a. Find the probability that the mean actual weight for the 100 weights is greater than 24.8. (Round your answer to four decimal places.
b. Find the 95th percentile for the mean weight for the 100 weights. (Round your answer to two decimal places.)
c. Find the 85th percentile for the total weight for the 100 weights. (Round your answer to two decimal places.
In: Statistics and Probability
Bicycles arrive at a bike shop in boxes. Before they can besold, they must be unpacked, assembled, and tuned(lubricated, adjusted, etc.). Based on past experience, the shop manager creates a model of how long this may take based on the assumptions that the times for each setup phase are independent, each phase follows a Normalmodel, and the means and standard deviations of the times in minutes are as shown in the table. Complete parts a) and b).
Phase Mean SD
Unpacking 3.5 .4
Assembly 22.1 2.8
Tuning 12.5 2.8
a) What are the mean and the standard deviation for the total bicycle setup time?
mean=38.1
SD=3.98
(Round to two decimal places as needed.)
b) A customer decides to buy one of the display models but wants a different color. The shop has one, still in the box. The manager says they can have it ready in half an hour. Do you think the bike will be set up and ready to go as promised? Explain.
(Round to four decimal places as needed.)
A.Yes, the probability that the bike will be ready in half an hour is ___________________
B.No, the probability that the bike will be ready in half an hour is __________________
The quarterly returns for a group of 68 mutual funds are well modeled by a Normal model with a mean of 5.6% and a standard deviation of 1.6%. Use the 68-95-99.7 Rule to find the cutoff values that would separate the following percentages of funds, rather than using technology to find the exact values.
a) the highest 50%
b) the highest 16%
c) the lowest 2.5%
d) the middle 68%
In: Statistics and Probability
In: Accounting
For a diabetic, the number of meals and quantity of calories in a day are very important to monitor. A diabetic monitored the number of times he eats in a day but since he leads a busy schedule he cannot always eat appropriately. Let X represent a discrete random variable of the number of meals that this diabetic consumes in a day. The following represents the probability distribution of X:
| X | 1 | 2 | 3 | 4 | 5 |
| P=(X=x) | 0.10 | 0.12 | 0.50 | 0.25 | 0.03 |
Find the probability that this diabetic eats at least 3 meals in a day.
Find the expected number of meals that the diabetic eats in a day.
Find the standard deviation of the number of meals that the diabetic eats in a day.
In: Statistics and Probability
An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 40% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)
(c) Suppose the probability distribution of the number of reservations made is given in the accompanying table.
| Number of reservations | 3 | 4 | 5 | 6 |
| Probability | 0.09 | 0.24 | 0.30 | 0.37 |
Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X.
| x | 0 | 1 | 2 | 3 | 4 |
| p(x) |
In: Statistics and Probability
The number of actual fire emergencies (emergencies where there is actually a fire) per week as the fire service in Bergen can be described with a Poisson distribution with parameter λ = 1.8. The time, measured in number of days, that goes between two subsequent real fire events is exponentially distributed with parameter λ = 1.8 / 7 = 0.26 (the time between subsequent events in a Poisson process is exponentially distributed). b) What is the expected number of days between two consecutive calls? What is the probability that there will be more than 1 day between two subsequent calls? What is the probability that less than 2 days will elapse between two subsequent calls? What is the probability that there will be between 1 and 2 days between two subsequent calls?
In: Statistics and Probability
The number of actual fire emergencies (emergencies where there is actually a fire) per week as the fire service in Bergen can be described with a Poisson distribution with parameter λ = 1.8. The time, measured in number of days, that goes between two subsequent real fire events is exponentially distributed with parameter λ = 1.8 / 7 = 0.26 (the time between subsequent events in a Poisson process is exponentially distributed). b) What is the expected number of days between two consecutive calls? What is the probability that there will be more than 1 day between two subsequent calls? What is the probability that less than 2 days will elapse between two subsequent calls? What is the probability that there will be between 1 and 2 days between two subsequent calls?
In: Statistics and Probability
The number of actual fire emergencies (emergencies where there is actually a fire) per week as the fire service in Bergen can be described with a Poisson distribution with parameter λ = 1.8. The time, measured in number of days, that goes between two subsequent real fire events is exponentially distributed with parameter λ = 1.8 / 7 = 0.26 (the time between subsequent events in a Poisson process is exponentially distributed). b) What is the expected number of days between two consecutive calls? What is the probability that there will be more than 1 day between two subsequent calls? What is the probability that less than 2 days will elapse between two subsequent calls? What is the probability that there will be between 1 and 2 days between two subsequent calls?
In: Statistics and Probability