X is a normally distributed random variable with mean 72 and standard deviation 22. Use calculator to find the probability indicated. a) P(78
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X is a
a) P(78<X<127)
b) P(60<X<90)
c) P(X=80) *continuous
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- The probability function of the amount of soft drink in a can is f(x)=4cx for11.5 <X< 12.5 oz. Determine the value of c such that f(x) represents a p.d.f..Then, find the following probabilities:(a) P(X > 11.5), (b) P(X < 12.25), and (c) P(11.75 <X< 12.25).Please show all work when answering this question. This is an ungraded question that is used for review so please help. This question refers to probabilityLet X denote a random variable having a distribution. If F(x)=ax³ where 0≤x≤(+3). Find f(x) after getting the constant value (a) and find the probability P(2Compute P(X) using the binomial probability formulaThen determine whether the normal distribution can be ed to estimate this probabilityIf soapproximate P(X) using the normal distribution and compare the result th the exact probability n=53, p = 0.7 and X = 41Suppose Y - Uniform(01, 02) where the parameters and 02 take the values 1 and 5 respectively. Compute the probability P(Y < y) when y=4.71.Q1A Suppose that the probability of finding defectives within a manufactured lot of electrical fuses is 0.09. Assume the probability distribution function (PDF) is binomial. Let X be the number of defectives within the sample. In a sample of 25 fuses, find the probabilities: (a) P(X 2), (b) P(X > 0), (c) P(1 ≤ X < 4). === B Suppose the discrete random variable X has the PDF as in the table below. Find: (a) F(7), (b) E(4-3X). I 4 6 7 8 9 f(x) 0.2 0.25 0.15 0.3 0.1X is a normally normally distributed variable with mean u =10 and standard deviation a =4. Find A) P(x 1) C) P(10poisson distributionFor each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfishPLEASE SHOW COMPLETE SOLUTIONFor the continuous random variable X, the probability distribution is given by a(x? + 1) f(x) = { 1sx<4 otherwise (a) Find i. The value of the constant a. ii. E(X). iii. Var(X) iv. P(1 sXs 3)x has continuous random variable is nomally distributed and average 40, standard deviation 10. So what is the probability of P (30SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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