Suppose that the probability of a successful optical alignment
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- 1a) Derive a maximum-liklihood estimator for the unknown parameter Y 1b) An experienced sales person completes sales following a Poisson distribution, with a mean rate of Y = 1.8 sales/month. A junior sales person completes sales at a mean rate of Y = 0.85 sales per month Find the probability of the joint sales team (experienced and junior) completing exactly 2 sales in any given months, assuming the two sales people act independently of each other. 1c) Find the probability of the joint sales team (experienced and junior) completing more than 2 sales in any given monthsA snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.Suppose that the probability of a successful optical alignment of an optical data storage product is 0.8. Assume that the trials is independent. a. Determine the probability mass function of the number of trials (X) required until the first successful alignment. b. Find the probability that the first successful alignment requires four trials at the maximum c. Calculate the mean and variance of X
- (a) A structure consists of 100 column footings. Suppose the settlement of eachfooting is exponentially distributed with a mean of 2 inches and the settlementsbetween footings are statistically independent. What is the probability that themaximum settlement Smax among the 100 footings will not exceed 5.0 inches?Compare this exact probability with the answer obtained assuming an appropriateasymptotic distribution for Smax b. What is the probability that the minimum settlement Smax is at least 0.5 inches? c. Determine the mean and coefficient ofvariation of the maximum differential settlement delta(max) defined as (Smax-Smin)The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?
- Suppose that the probability of a successful optical alignment in the assembly of an optical data storage product is 0.9. Assume that the trials are independent. a. Determine the probability mass function of the number of trials (x) required until the first successful alignment. b. Find the probability that the first successful alignment requires trials four trials at the maximum. c. Calculate the mean and variance of x.The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 L.E and a variance of 900 L.E2. 1) If the management wants to give free gifts to at most 12% of the customers, what should the amount of expenditure be above which a customer would receive a free gift? 2) In a sample of 100 customers, what is the number of customers whose expenditure is between 420 L.E and 485 L.E? 3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 L.E? 4) What is the percentage of customers whose expenditure is at least 450 L.E.?The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 L.E and a variance of 900 L.E2.1) If the management wants to give free gifts to at most 12% of the customers, what should the amount of expenditure be above which a customer would receive a free gift?
- Suppose that the probability of a successful optical alignment in the assembly of an optical data storage product is 0.6. Assume that the trials are independent a. Find the probability that the first successful alignment requires trials four trials at the maximum b. Calculate the mean of x c. Calculate the variance of xA travel association says the daily lodging costs for a family in the United States is $132. You work for a tourist publication and want to test this claim. You randomly selected 10 U.S. families and find out how much each spent on lodging for one overnight trip. At alpha=0.02, can you reject the travel association's claim? (Adapted from the American Automobile Association) 164 137 142 155 119 104 74 204 148 181 Assume the population is normally distributed.Assume the probability that a maple tree at age 5 grows less than 150 cm is equal to 0.3. If the height of maple trees at age 5 are estimated to be normally distributed with mean u cm and variance 64 cm. find u.
