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- Consider that the annual demand of a product is uniformly distributed between 200 and 300 units. Profit per unit sold is 10,000 rupee and the annual cost can be assumed to be constant at 23,00,000 rupee. Obtain distribution and density functions of random profit. Also, obtain the mean, variance, standard deviation, and median of profit.Anticipated consumer demand in a restaurant for free-range steaks next month can be modeled by a normal random variable with mean 1,200 pounds and standard deviation 100 pounds. a. What is the probability that demand will be between 1,100 and 1,300 pounds? Calculate in 4 decimal place. b. The probability is 0.10 that demand will be more than how many pounds?Question 15 Suppose X is a random variable taking values 0, 1, 2, 3, 4, 5 with equal probability. What is the variance of X?
- 3. A salesman who frequently drives from Muscat to Sohar finds that his driving time is a random variable having roughly a normal distribution with mean 4.3 hours and standard deviation 0.2 hour. Find the probabilities that such a trip will take a. more than 4.0 hours, b. less than 5.0 hours. C. Between 3.5 and 5.5 hoursThe owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: SIZE OFOUTLET DEMAND LOW HIGH Small $ 1,000 1,000 Medium 500 2,500 Large 0 3,000 For what range of probability that demand will be high, will she decide to lease the medium facility?The time taken to complete a bicycle race is normally distributed, with anaverage time (μ) of 2.25 hours and a standard deviation (σ) of 0.65 hours.What is the probability that a randomly selected cyclist will: Q.7.3.1 Take between 2.75 and 3.15 hours to complete the race? Interpretyour answer. Q.7.3.2 Take between 2.05 and 2.15 hours to complete the race? Interpretyour answer.
- Suppose there are n assets which are uncorrelated. (They mightbe n different “wild cat” oil well prospects.) You may invest in any one, or in any combination of them. The mean rate of return r¯ is the same for each asset, but the variances are different. The return on asset i has a variance of σ2i for i = 1, 2, . . . , n.(a) Show the situation on an r¯-σ diagram. Describe the efficient set.(b) Find the minimum-variance point. Express your result in terms of σ¯2 =!"ni=11σ2i#−1.Two types of light bulbs are manufactured by firm A and firm B. The life of bulb type A is normally distributed with mean 100 hours and variance 15. The life of bulb type B is normally distributed with mean 105 hours and variance 30. (i) What is the probability that a type A bulb will last more than 110 hours? (ii) If 20 bulbs each of type A and type B bulbs are turned on at the same time, what is the probability that type A bulbs will last longer than type B bulbs ?1. Suppose the prices of used cars in the market are normally distributed with a mean of $15,000 and a standard deviation of $7,5000. What is the probability of selecting a car from this market and its priced above $20,000.
- A pizza delivery service delivers to a campus dormitory. Delivery times follow a normal distribution with a mean of 20 minutes and a standard deviation of 4 minutes.a. What is the probability that a delivery will take between 15 and 25 minutes?b. The service does not charge for the pizza if delivery takes more than 30 minutes. What is the probability of getting a free pizza from a single order?c. During final exams, a student plans to order pizza five consecutive evenings. Assume that these delivery times are independent of each other. What is the probability that the student will get at least one free pizza?d. Find the shortest range of times that includes 40% of all deliveries from this service.e. For a single delivery, state in which of the following ranges (expressed in minutes) the delivery time is most likely to lie.18-20, 19-21, 20-22, 21-23f. For a single delivery, state in which of the following ranges (expressed in minutes) the delivery time is least likely to lie.18-20,…According to a 2017 Wired magazine article, 40% of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (Wired magazine website). Suppose we randomly select 50 received e-mails. a. What is the expected number of these e-mails that are tracked? b. What are the variance (to the nearest whole number) and standard deviation (to 3 decimals) for the number of these e-mails that are tracked? Variance Standard deviationYou work at a mechanic shop. On average, 10 cars come into your shop each day. Assuming a poisson distribution, what is the probability 4 cars come into the shop? Round to 4 decimal points.