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

Answer 1

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:

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

Now, we have to evaluate

$P(x$

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.