A company which produces jelly beans claims that the amount, in ounces, of jelly beans in their bags is uniformly distributed on the interval 14 to 18 ounces.
(a) On average, how many ounces of jelly beans are there in a bag? What is the standard deviation?
(b) Assuming that the claim of the company is true, what is the probability that a randomly selected bag contains less than 16.25 ounces?
c) A consumer watch group wants to investigate the claim of the company. They collect a random sample of 40 bags of jelly beans and find that the average number of ounces per bag is 15.6. Assuming that the claim of the company is true, what is the probability that a sample of 40 bags has an average of less than 15.6 ounces of jelly beans per bag. Interpret this result in the context of the problem. What does this indicate about the plausibility of the claim made by the company? You must justify and explain all of your calculations and conclusions.
In: Statistics and Probability
1. Igor Beaver is a salesman for Planet of the Grapes, a medium sized winery near Solvang. Igor is going on a sales trip visiting 10 restaurants throughout Southern California. Historically, Igor convinces 30% of the restaurants he visits to stock and sell his wine. a. What is the expected number of restaurants that Igor will close a sale on this trip? b. Find the variance. What is the probability that on this sales trip Igor make sales at c. 4 restaurants or less? d. Between 2 and 4 restaurants? e. Exactly 4 restaurants? f. At least 5 restaurants? g. Igor gives each new client a gift. How many gifts should he take on the trip to be at least 99% sure that he has enough? h. Find and plot the probability distribution and cumulative distribution using Excel.
In: Math
Liam is a professional darts player who can throw a bullseye 70%
of the time.
If he throws a dart 250 times, what is the probability he hits a
bulls eye:
a.) At least 185 times?
b.) No more than 180 times?
c.) between 160 and 185 times (including 160 and 185)?
Use the Normal Approximation to the Binomial distribution to answer
this question.
2. A recent study has shown that 28% of 18-34 year olds check
their Facebook/Instagram feeds before getting out of bed in the
morning,
If we sampled a group of 150 18-34 year olds, what is the
probability that the number of them who checked their social media
before getting out of bed is:
a.) At least 30?
b.) No more than 51?
c.) between 35 and 49 (including 35 and 49)?
Use the Normal Approximation to the Binomial distribution to answer
this question.
In: Math
|
Good Time Company is a regional chain department store. It will remain in business for one more year. The probability of a boom year is 80 percent and the probability of a recession is 20 percent. It is projected that the company will generate a total cash flow of $199 million in a boom year and $90 million in a recession. The company's required debt payment at the end of the year is $124 million. The market value of the company’s outstanding debt is $97 million. The company pays no taxes. |
| a. |
What payoff do bondholders expect to receive in the event of a recession? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.) |
| b. | What is the promised return on the company's debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) |
| c. | What is the expected return on the company's debt? |
In: Finance
The UDairy ice cream truck plans to sell ice cream at an upcoming alumni event in Central Park (NYC). From past events, demand for ice cream is highly weather dependent. On rainy days, demand is normally distributed with a mean of 120 scoops and standard deviation of 35 scoops. On non-rainy days, demand is normally distributed with a mean of 200 scoops and standard deviation of 60 scoops. The ice cream truck will be loaded two days before the event and travel to NYC. If the UDairy truck plans to bring enough ice cream to maintain a 90% service level for a rainy day, but the day surprisingly turns out to be non-rainy, what is the probability of the ice cream truck stocking out? For simplicity, assume the number of scoops demanded is a continuous variable. Enter probability as a three-digit decimal (e.g. 0.500, 0.275, 0.942).
In: Math
In product design for human use and recommended guideline for the product’s human use, it is important to consider the weights of people so that airplanes or elevators aren’t overloaded. Based on data from the National Health Survey, the weight of adults in the United States has a mean of 181 pound (the average of 195.5 for males and 166.2 for females, assuming, arbitrarily, equal male and female population) with a standard deviation of 30 pounds. An airplane is designed to have a human carrying maximum-capacity 18,500 pounds. An Airline adopts the operation procedure of maximum passenger number (n), based on the concept of the probability of a randomly selected n passengers exceeding the maximum-capacity to be less than 0.01 (i.e., 1%). a) [3 pts] Determine n b) b) [2 pts] What will be the value of n if the probability of exceeding the maximum-capacity is no more than 0.001 (i.e., 0.1%)?
In: Math
What is probability distribution?
a. Select 5 probability distributions from discrete and continuous random varibles. Express the probability function and distribution functions of these distributions.
b. Show that the distributions you select fulfill the conditions for the probability functions to be probability functions.
c. Find the expected values and variance of these distributions theoretically.
In: Statistics and Probability
Expected Returns: Discrete Distribution
The market and Stock J have the following probability distributions:
| Probability | rM | rJ |
| 0.3 | 12% | 21% |
| 0.4 | 10 | 4 |
| 0.3 | 17 | 12 |
a.Calculate the expected rate of return for the market. Round
your answer to two decimal places.
%
b. Calculate the expected rate of return for Stock J. Round your
answer to two decimal places.
%
c. Calculate the standard deviation for the market. Round your
answer to two decimal places.
%
d. Calculate the standard deviation for Stock J. Round your answer
to two decimal places.
%
In: Finance
Conditional Probability
Problem 1 Conditional probability
In group of 200 university students, 140 are full time students (80 females and 60 males) and 60 no full time students (40 females and 20 males).
Let
M=event a student is male
W=event a student is a female
F=event a student is full time
FC= event a student is not full time
1) Find the probability that a student is male and full time
2) Find the probability that a student is male and is not full time
3) Find the probability that a student is female and full time
4) Find the probability that a student is female and not full time
5) Find complete the following
Table1.1: Joint probability table for full time student
|
Full time |
Not full time |
Total |
|
|
Male |
|||
|
Female |
|||
|
Total |
6) Find the conditional probabilities
6.1)the probabilities of full time for a male student
6.2) the probabilities of full time for a female student
In: Statistics and Probability
What is probability? Describe classical, empirical, and subjective probability, and provide "real-world" examples of each. How can each of these types of probability apply to the business world? Do you think any one type is more useful in business than the others? Why or why not?
In: Statistics and Probability