3 ot,15 (11 complete) This Quiz: 15 pts pe Question Help Use n 9, and p 0.5 to c

Question

3 ot,15 (11 complete) This Quiz: 15 pts pe Question Help Use n 9, and p 0.5 to complete parts (a) through (c) below (a) Find the probabilities and construct a binomial probability distribution with the given parameters. (b) Compute the mean and standard deviation of the random variable. (c) Draw the probability histogram, comment on its shape, and label the mean on the histogram (a) To construct a binomial probability distribution, complete the table to the right Round to four decimal places as needed.) (b) Compute the mean and standard deviation of the random variable Click to select your answer(s)- 11:59pm

Explanation / Answer

a.
P( X = 0 ) = ( 9 0 ) * ( 0.5^0) * ( 1 - 0.5 )^9
= 0.002
P( X = 1 ) = ( 9 1 ) * ( 0.5^1) * ( 1 - 0.5 )^8
= 0.0176
P( X = 2 ) = ( 9 2 ) * ( 0.5^2) * ( 1 - 0.5 )^7
= 0.0703
P( X = 3 ) = ( 9 3 ) * ( 0.5^3) * ( 1 - 0.5 )^6
= 0.1641
P( X = 4 ) = ( 9 4 ) * ( 0.5^4) * ( 1 - 0.5 )^5
= 0.2461
P( X = 5 ) = ( 9 5 ) * ( 0.5^5) * ( 1 - 0.5 )^4
= 0.2461
P( X = 6 ) = ( 9 6 ) * ( 0.5^6) * ( 1 - 0.5 )^3
= 0.1641
P( X = 7 ) = ( 9 7 ) * ( 0.5^7) * ( 1 - 0.5 )^2
= 0.0703
P( X = 8 ) = ( 9 8 ) * ( 0.5^8) * ( 1 - 0.5 )^1
= 0.0176
P( X = 9 ) = ( 9 9 ) * ( 0.5^9) * ( 1 - 0.5 )^0
= 0.002

b.
Mean ( np ) =9 * 0.5 = 4.5
Standard Deviation ( npq )= 9*0.5*0.5 = 1.5

c.
Option A

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