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- The mean µ=np and the standard deviation σ = np(1−p) is forPorphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 43 and standard deviation ? = 9. Find the following probabilities. (a) x is less than 60(b) x is greater than 16(c) x is between 16 and 60(d) x is more than 60The random variable X has a distribution function:F(x) = 0 ; x < 3 = 1/c(x2 - 3x) ; 3 <= x <=6 = 1 ; x > 6 Count the value of constant "c" Count the P(X > 4) and P(5 <= X <= 6) Count the median of X Thanks for help!
- If XX represents a random variable coming from a normal distribution and P(X<10.2)=0.22P(X<10.2)=0.22, then P(X>10.2)=0.78P(X>10.2)=0.78. true or falseLet x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean ? = 81 and estimated standard deviation ? = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed. (b) Suppose a doctor uses the average xbar for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1. - select one of the choices in screenshot What is the probability that x < 40? (Round your answer to four decimal places.) Explain what this might imply if you were a doctor or a nurse. - select one of the choices in screenshotHow do you find the mean and variance of part(d)?I need the detailed solution.'Melanoma' is a form of skin cancer and each year 17% of the patients who suffer from the disease die. A random sample of 10,000 melanoma patients is formed at the start of a year. Let Y denote the number of patients in this sample who will die during the year? (a) What is the expected value of Y? That is, compute E(Y). Answer: [Select] (b) What is the variance of Y? That is, compute var(Y). Answer: [Select] (c) What is the probability that Y exceeds 1,800? That is, compute P(Y> 1,800). Answer: [Select]A proton emitter produces proton beams with changing kinetic energy that is uniformly distributed between three and eight joules. Suppose that it is possible to adjust the upper limit of the kinetic energy (currently set to eight joules). • What is the mean kinetic energy? What is the variance of the kinetic energy? What is the probability that a proton beam has a kinetic energy of exactly 3.5 joules? a. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a continuous distribution O b. E(X) = 5, V(X) = 1.33, probability is zero (0) because X has a uniform distribution O c. NONE O d. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a uniform distributionX is distributed as a Normal random variable with mean of 100 and a standard deviation of 10 (i.e X~N(100,10). You take a random sample of 20 items from X and you calculate the average of this sample. What is the expected value of this sample average? (i.e. what value would you expect to get for the average of this small sample?