This Question: 1 pt 26 of 30 (21 complete) is Test: 30 pts po Question Help * As

Question

This Question: 1 pt 26 of 30 (21 complete) is Test: 30 pts po Question Help * Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean and standard deviation Also, use the range rule of thumb to find the minimum usual value -2 and the maximum usual value 2 n=90, p:075 = (Round to one decimal place as needed.) _ 2 (Round to one decimal place as needed.) +2 ] (Round to one decimal place as needed) Enter your answer in each of the answer baxes 7:10 PM

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
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 90 * 0.75
= 67.5
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 90 * 0.75 * 0.25
= 16.875
III.
standard deviation = sqrt( variance ) = sqrt(16.875)
=4.10792

Answers:
mean(u) = 67.5
standard deviation() = 4.1
u-2* = 67.5 - 2*4.10792 = 59.2
u+2* = 67.5+2*4.10792 = 75.7

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