# Based on his past record, Luke, an archer for a college archeny practice L auke wesent the number on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner Assume that in one practice Luke will attempt 5 shots ers. Let the random variable X represent the number of times he hits ring of the target with a shot of the arrow. Assume that each shot is independent from the Let team varable of the arrow and in attempts. The probability distribution of X is given in the table.

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## Question:

Based on his past record, Luke, an archer for a college archeny practice L auke wesent the number on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner Assume that in one practice Luke will attempt 5 shots ers. Let the random variable X represent the number of times he hits ring of the target with a shot of the arrow. Assume that each shot is independent from the Let team varable of the arrow and in attempts. The probability distribution of X is given in the table. P(X) 0 000001 0,00045 0.00810 0.07290 03280S 0.59049
What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X?
(A) 0.40951
(B) 0.50000
(C) 0.59049
(D) 0.91854
(E) 0.99144

Option (A) 0.40951

Step-by-step explanation:

We are given the following information in the question:

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P(target) = 0.90

Let the random variable X represent the number of times he hits ring of the target with a shot of the arrow.

The probability distribution of X is

x:         0              1                2               3               4               5

P(x):    0.00001   0.00045  0.00810   0.07290   0.32805   0.59049

The mean of discrete probability distribution is given by:

Now, we have to evaluate

Option (A) 0.40951 t is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X.

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