Examine the probability distribution shown below. Complete parts a through d. Ca

Question

Examine the probability distribution shown below. Complete parts a through d. Calculate the expected value and standard deviation for this random variable. E(x) = (Type an integer or a decimal.) sigma_x = (Round to two decimal places as needed.) Denote the expected value as meu Calculate meu - sigma and meu + sigma. Meu - sigma = (Round to two decimal places as needed.) meu + sigma = (Round to two decimal places as needed.) Determine the proportion of the distribution that is contained within the interval meu plus or minus sigma. (Type an integer or a decimal.) Repeat part c for (1) meu plus or minus 2sigma and (2) meu plus or minus3sigma. Determine the proportion of the distribution that is contained within the interval meu plus or minus 2sigma. (Type an integer or a decimal.) Determine the proportion of the distribution that is contained within the interval meu plus or minus 3sigma. (Type an integer or a decimal.)

Explanation / Answer

a.) E(x) = x * P(x)

µ = 25.65

  x = (E(x2) - [E(x)]2)

= 25.36

b) µ - = 0.281

µ + = 51.01

P(µ +) - P(x>µ - ) = P(µ +) - (1 - P(x<µ - ))

We can calculate it using normal distribution table = 0.6828

d.) 1.) µ - 2 = -25.08

µ +2 = 76.38

P(µ +2) - P(x>µ - 2) = P(µ +2) - (1 - P(x<µ - 2))

We can calculate it using normal distribution table = 0.9545

2.) µ - 3 = -50.45

µ +3 = 101.75

P(µ +3) - P(x>µ - 3) = P(µ +3) - (1 - P(x<µ - 3))

We can calculate it using normal distribution table = 0.5799

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