Question

The probability of an archer hitting a target with a bow and arrows is 2/3. The archer shoots 15 times. Let random variable X be the number of successful shoots. Find the expected value and the standard deviation for X.

Answer 1

Given :- probability that tha archer hitting a target with a bow and arrows = 2/3

And archer shoots 15 times.

p=2/3 , n=15

Therefore, q= 1- p =1/3

Here the probability that the archer hit a target with a bow and arrows is constant and number of trials is finite. Therefore, in this question we use binomial distribution.

Solution :-

X is a binomial random variable.

Therefore , expected value of binomial distribution is given as :-

E(x) = n p

= 2/3 × 15 = 10

And standard deviation of binomial distribution is given as :-

S.D = square root of ( n p q)

S.D = square root of ( 15. 2/3. 1/3) {where n=15, p=2/3 ,q=1/3 }

S.D = square root of (3.333) =1.825

Hence, mean is 10 and standard deviation is 1.825.

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