Homework: Week 3 Homework 40 pts Score: 0 ot 5 pts 3.2.23 HW Score: 51.88%, 20 7

Question

Homework: Week 3 Homework 40 pts Score: 0 ot 5 pts 3.2.23 HW Score: 51.88%, 20 75 of 40 pts n a sample of 900 U.S adults, 214 dine out at a resaurant more than once per week Two U.S adults are sellected at random trom the population of all U S adults without seplacement Assuming the sample is repesentative of U S adults, complete parts (a) through (d a) Find the probability that both aduhs dine out more than once per week The probablity that both adults dine out more tan once per week is Round to three decimal places as needed ) 3 1017 °Type here to search

Explanation / Answer

BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials   
n = is the number of independent trials   
p = probability of success on each trial

p = 214/900 = 0.23778
X ~ B ( 2, 0.23778)
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 2 * 0.23778
= 0.47556
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 2 * 0.23778 * 0.76222
= 0.362481
III.
standard deviation = sqrt( variance ) = sqrt(0.362481)
=0.602064

P( X = 2 ) = ( 2 2 ) * ( 0.23778^2) * ( 1 - 0.23778 )^0
= 0.056539

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