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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

Respuesta :

Answer:

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:

[tex]\mu = \displaystyle\sum x_iP(x_i)\\\\= 0(0.00001) + 1(0.00045) + 2(0.00810) + 3(0.07290) + 4(0.32805) + 5( 0.59049)\\= 4.5[/tex]

Now, we have to evaluate

[tex]P(x<\mu)\\=P(x<4.5)\\=P(x =0) + P(x =1) + P(x =2) + P(x =2) + P(x =3) + P(x =4)\\= 0.00001 + 0.00045+0.00810+0.07290+0.32805\\=0.40951[/tex]

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:

[tex]\mu = \; \in x_i p (x_i)\\ \\= 0 (0.0001) + 1 (0.0045) + 2 (0.00810) + 3 (0.07290) + 4 ( 0.3280) + 5(0.59049)\\\\= 4.5[/tex]

Now, we have to evaluate

[tex]= p (x <\mu)\\\\= p( x<4.5)\\\\\ = p( x = 0 ) + p ( x = 1 ) + p ( x = 2 ) + p ( x = 3 ) + p ( x = 4 )\\\\[/tex]

= 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 .

For details about probability distribution click the link given below;

https://brainly.com/question/14210034

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