Assignemnt: Data Analytics Problems
1. Based on historical data, sales for a particular cosmetic line follow a continuous uniform distribution with a lower limit of $2,500 and an upper limit of $5,000.
A. What are the mean and standard deviation of this uniform distribution?
B. What is the probability that sales exceed $4,000?
2. Many people apply for jobs to serve as paramedics or firefighters, yet they cannot complete basic physical fitness standards. A study found that 77% of all candidates for paramedic and firefighter positions were overweight or obese.
A. What is the expected value and the standard error of the sample proportion derived from a random sample of 100 candidates for paramedic or firefighter positions?
b. What are the expected value and the standard error of the sample proportion derived from a random sample of 200 candidates for paramedic or firefighter positions?
3. The scheduled arrival time for a daily flight from Boston to New York is 9:25 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:15 am and a late arrival time of 9:55 am.
a. Calculate the mean and the standard deviation of the distribution.
b. What is the probability that a flight arrives late (later than 9:25 am)?
c. Vee Products Company is investigating the possibility of producing and marketing backyard storage sheds.
d. Undertaking this project would require the construction of either a large or a small manufacturing plant. Vee, of course, has the option of not developing the new product line at all.
e. The market for the product produced-storage sheds-could be either favorable or unfavorable. Probability - 0.6 favorable and 0.40 unfavorable market.
f. A.Construct a Decision tree,
g. B.Construct a Decision Table showing market for product produced,
h. C.Calculate Maximax, Maximin and equally likely,
i. D.Construct a Decision Table under uncertainty,
j. E.Determine the expected monetary value (EMV) for each alternative.
4. The mean height of adult men in the u.s is 69.7 inches, with a standard deviation of 3 inches.
(a) A sociologist believes that taller men may be more likely to be promoted to position of leadership, so the mean height µ of male business executives may be greater than the mean height of the entire male population.
(b) A simple random of 100 male business executives has a mean height of 69.9in. Assume that the standard deviation of male executive heights is α=3 inches . Can we conclude that the male business executives are taller on average than the general male population at the α= 0.05 level
5. Scientists want to estimate the mean weight of mice after they have been fed a special diet. From previous studies, it is known that the weight is normally distributed with standard deviation 3 grams. How many mice must be weighed so that a 95% confidence interval will have a margin of error of 0.5 grams?
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also include a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also Include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.