16. Let X be normally distributed with mean μ = 120 and standard deviation σ = 20. a. Find P(X86). b. Find P(80 ≤x≤ 100). ة ن فـ d. Find x such that P(X ≤x) = 0.40. Find x such that P(X>x) = 0.90.
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- CBS news reported that 4% of adult Americans have a food allergy consider selecting 10 adult Americans at random define the variable x as: x= number of people in the sample of 10 that have a food allergy a. p(x<3) b. p(x lesss than or equal to 3) c. p (x greater than or equal to 4) d. p (1 less than or equal to x less than or equal to 3)Please help with parts a,b,c,d, and if possible e!I need help with parts “c”, “d, and “e” thanks.
- Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is randomly drawn from a uniform distribution on the interval [90, 210], where the unit is U.S. million dollars. In addition, suppose that after the value X = x has been observed (90 < x < 210), the 2023 team budget, say Y, is randomly drawn from a uniform distribution on the interval [x, 210]. In other words, the 2023 budget is at least as large as the 2022 budget. (a) For any given value of x (90 < x < 210), obtain E[Y|X = x]. (b) In view of part (i), obtain E[Y|X]. (c) What is the difference between E[Y|X = x] and E[Y|X]? (d) Obtain E[Y]. That is, what is the expected value of your 2023 fantasy basketball budget? (e) Golden State Warriors won the 2022 NBA finals. Their estimated 2022 payroll is about $194 million. Would your 2023 fantasy basketball budget be on average larger than Golden State Warriors' 2022 payroll? Explain briefly.6 The blood pressure of a diabetic taken at random has a normal distribution with mean 126 and variance 60. The blood pressure of a non-diabetic taken at random has a normal distribution with mean 121 and variance 40. Let X d be the average blood pressure of four diabetics taken at random and X n be the average blood pressure of four non-diabetics taken at random. Find Prob( X d > X n). Hint: Define D by D= X d - X n, find the mean and the variance of D and then calculate the probability that D>0.3. If X is x² (23), find the following: a) P(14.85 < X < 32.01) b) constants a and b such that P(a < X < b) = 0.95 and P(XSuppose that Yt is the monthly value of the number of new home construction projects started in the United States. Because of the weather, Yt has a pronounced seasonal pattern; for example, housing starts are low in January and high in June. Let μJan denote the average value of housing starts in January and let μFeb, μMar,. . . . , μDec denote the average values in the other months. Show that the values of μJan, μFeb, . . . , μDec can be estimated from the OLS regression Yt = β0 + β1Febt + β2Mart + . . . .+ β11Dect + ut, where Febt is a binary variable equal to 1 if t February, Mart is a binary variable equal to 1 if t is March, and so forth.Let XX represent the full height of certain species of tree. Assume that XX is normally distributed with a mean of 217 feet and a standard deviation of 34 feet.Find the probability that the full height of a randomly selected tree is less than 248 feet. P(X<248)P(X<248) = Enter your answer as a number accurate to 3 decimal places.EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.SEE MORE QUESTIONS
