You must show some work for this problem such as showing what formula you are us

Question

You must show some work for this problem such as showing what formula you are using and where variables are "plugged in." Definitely use your calculator for the hard calculations and/or to check your work! According to the 2011-2012 data set report, 45% of MSU Denver undergraduates are age 25 or older. randomly selected MSU Denver undergraduates, find the probability that the number, X, who are age 25 or older is: a. (2 pts) Exactly three. 1. b. (2 pts) At least one. (Hint: think about what numbers this includes. Several ways to do this one!) c. (2 pts) Find the mean of the binomial random variable. d. (2 pts) Find the standard deviation of the binomial random variable.

Explanation / Answer

X ~ Binomial (n,p)

Where n = 8 , p = 0.45

Binomial probability distribution is

P(X) = nCx px (1-p)n-x

a)

P( X = 3) = 8C3 0.453 0.555

= 0.2568

b)

P( X >= 1) = 1 - P( X = 0)

= 1 -  8C0 0.450 0.558

= 1 - 0.0084

= 0.9916

c)

Mean = n * p

= 8 * 0.45

= 3.6

d)

Standard deviation = Sqrt( n p ( 1 -p) )

= Sqrt( 8 * 0.45 * 0.55)

= 1.4071

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