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 1 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) 0.5
(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:

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.

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  is 0.40951 .

Given that ;

Probability of hitting the inner P(target) = 0.90

According to given question;

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

= 0.000001 + 0.00045 + 0.00810 + 0.07290 + 0.32805

=  0.40951

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  is 0.40951 .

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