SP Q5: Suppose that X₁ and X₂ are independent random variables each having a standard normal distribution Find the joint p.d.f. of
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A: Answer: From the given data, Mean μ = 100 Standard deviation σ = 15 For a sample size of n = 64
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A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…
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A: Mean=140, Standard deviation=10
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A: Plug in all the values in the formula, we get
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A: The joint probability mass function of X and Y is given as:X-1001000.20.10Y10.10.2020.10.10.2
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A: We are given two normal distributions with mean = 0 and standard deviations σ1 and σ2.
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- A factory produces cylindrical metal bar. The production process can be modeled by normal distribution with mean length of 11 cm and standard deviation of 0.25 cm. (a) What is the probability that a randomly selected cylindrical metal bar has a length longer than 10.5 cm? (b) There is 14% chance that a randomly selected cylindrical metal bar has a length longer than K. is the value ofK? What (c) The production cost of a metal bar is $80 per cm plus a basic cost of $100. Find the mean, median, standard deviation, variance, and 86th percentile of the production cost of a metal bar. (d) Write a short paragraph (about 30 - 50 words) to summarize the production cost of a metal bar. summary needs to include all summary statistics found in part (c)). (The (e) In order to minimize the chance of the production cost of a metal bar to be more expensive than $1000, the senior manager decides to adjust the production process of the metal bar. and can't be changed while the standard deviation can be…Suppose that X has a Weibull distribution with β = 2 and δ = 2400. Determine the following. a. P(X > 5000) = b. For an exponential random variable with the same mean as the Weibull distribution P(X > 5000) =Z denote a random variable following the standard normal distribution. Pr(Z>1.8) = ?
- please solve question 11Weights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.If continuous random variable normally distributed with mu = 256.43 and J = 27.11 , what is P(225.75 <= x <= 300.35) ?
- Given two normal random variables: X-Normal(u=6,0-15) and Y-Normal(u=15,0=3). What can be said about the points x-21 and y=21 when plotted in a STANDARD normal distribution? [Select] [ Select] x and y both lie on the right side of the distribution x and y are equal x and y both lie on the left side of the distribution • Previous x is to the right of y Next >A random sample of size n = 28 is obtained from a normally distributed population with a population mean of u = 350 and a variance of o =145. a. What is the probability that xr < 345? b. What is the probability that the sample variance is less than 140? c. What is the probability that the sample variance is greater than 175?Suppose the random variable X follows a binomial distribution with n = 0.50. Using the normal approximation, what is the value for P(X > 38)? 100 and p =
- level of blood glucose and diabetes are closoly related. Let x bo a random variable measured in milligrams of glucose per deciliter of od. After a 12-hour fast, th random variable x will have a distribution that is approximately normal with mean - 85 and standard deviation 5. What is the probability that for an adult after a 12-hour fast. s less than 7o, b. x is greater than 120?Suppose the random variable Z follows a standard normal distribution,, Then thevalue of PIZ<-339) is O A 0.9997 O B. 0,0003 O C. 1.000 O D. 0.0000Please answer both parts of the question thanks