-11.11 points 3.E.068. My Notes O Ask Your Tea Sixteen individuals are scheduled

Question

-11.11 points 3.E.068. My Notes O Ask Your Tea Sixteen individuals are scheduled to take these individuals are randomly assigned to a particular examiner, and let X be the number among the six who are taking the test for the first a driving test at a particular DMV office on a certain day, nine of whom will be taking the test for the first time. Suppose that six of (a) What kind of a distribution does X have (name and values of all parameters)? 9 b(x; 6,15 b(x; 6, 9,16) nb(x; 6, 9, 16) h(x; 6, 16 O h(x; 6, 9,16) (b) Compute-4), por s 4), and P(X 4). (Round your answers to four decimal places.) P(X S4) (c) Calculate the mean value and standard deviation of x. (Round your answers to three decimal places) mean individuals standard deviation ndividuals

Explanation / Answer

Answers below:

We can model this using binomial distribution. All we have to do first is find the distribution' params:

a.

Binomial distribution' params are n and p where n in this case is the no. of trials or 6
p = no. of people tested for 1st time / no. of total people = 6/19

So, b(x;6,9/16 ) is the right answer.

So, 2nd option is right

b.P(X=4) = 6C4(9/16)^4 ( 1-9/16)^2 = 0.2874
P(X<=4) = = P(X=0,...4) = 6C4(9/16)^0 ( 1-9/16)^6+....6C4(9/16)^4 ( 1-9/16)^2 = .8206
P(X>=4) = = P(X=4,...6) = 6C4(9/16)^4 ( 1-9/16)^2+....6C6(9/16)^6 ( 1-9/16)^0 = .4669

c.
Mean = np = 6*9/16 = 3.375
Standard deviaation = sqrt(npq) = sqrt( 6*9/16 * 7/16) = 1.215

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