The continuous random variable T denotes the time in hours that employees devoteon overtime. The cumulative distribution function of T is(a)(b)(c)(d)(e)Show that m=16270,t<0,m (213-14), 0≤t≤ 1.5,t> 1.5.Find E(T).F(t) = m1,Find the proportion of employees who devote more than 1 hour on overtime.Find the probability density function f(t) of T.11An employee is chosen at random. Calculate the probability that the employeedevoted more than 1 hour on overtime, given that the employee devoted morethan the mean amount of time on overtime.

As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted.....…

Answered: The continuous random variable T…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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you should calculate the required probabilities using tables A model for normal human body temperature, X, when measured orally in F, is that it is normally distributed, X N(98.2, 0.5184). According to the model, what proportion of people have a normal body temperature of 99 F or more? (0) (i) Find the normal body temperature such that, according to the model, only 10% of people have a lower normal body temperature. (ii) Let W denote normal human body temperature, when measured orally in C. Given that W =59 (X-32) and X N(98.2, 0.5184), what is the distribution of W?
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A model for normal human body temperature, X, when measured orally in °F, is that it is normally distributed, X ~ N (98.2,0.5184). (i) According to the model, what proportion of people have a normal body temperature of 99 °F or more? (ii) Find the normal body temperature such that, according to the model, only 10% of people have a lower normal body temperature. (iii) Let W denote normal human body temperature, when measured orally in °C. Given that W = (X - 32) and X ~ N(98.2,0.5184), what is the distribution of W? (iv) According to the model that you just derived for W, what proportion of people have a normal body temperature of between 36 °C and 36.8 °C?
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The probability distribution of the binomial random variable X is 3-x b(x; n, p) = (³) (¹) * (-²) ³**. x = 0,1,2,3. The standard deviation of X may be expressed as a simplest fraction equal to Find (a + b)².
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