O RANDOM VARIABLES AND DISTRIBUTIONS Shasia Standard normal probabilities Let z be a standard normal random variable. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. |(a) P(Z<-1.15) = [ (b) P(z> -1.29) = [ (c) P(0.85 < Z < 2.18) = [] Explanation Check Terms of Use Privacy I Accessihilitu AH Dishte Deeoned

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A: Given data is x 1 2 3 4 5 f(x) 0.3 0.18 0.06 0.14 0.32

Q: From the figure, what is P(X > 1.32) or P(X < 0.02)? Do not round.

A: GIVEN DATA, uniform distribution X~U(0,1)we have to find out the p(X&gt;1.32) or p(X&lt;0.02)=?

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Q: P(z -1.16) = P(z 2.61) = P(0 < z < 2.32)

A: We will use Standard Normal table to find the required probabilities.

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A: P(1.15&lt;z&lt;3.36)=?

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!