Question

It is known that a certain lacrosse goalie will successfully make a save 80% of the time. (Assume that all save attempts are independent.) Suppose that the lacrosse goalie attempts to make 12 saves. (Round answers to three decimal places.) (a) What is the probability that the lacrosse goalie will make at least 10 saves

Answer 1

Answer:

The probability is  $P(X \ge 10 ) = 0.558$  

Step-by-step explanation:

From the question we are told that

   The  probability of making a successful save is  p =  0.80

    The sample size  n  =  12

Generally the distribution of number of saves made by the lacrosse goalie follows a binomial distribution  

i.e  

         $X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial  distribution is  

      $P(X = x) = ^{n}C_x * p^r * (1- p)^{n-r}$

Here C stands for combination hence we are going to be making use of the combination function in our calculators  

 Generally the probability that  the lacrosse goalie will make at least 10 saves

is mathematically represented as

   $P(X \ge 10 ) = P(X = 10 ) + P(X = 11 ) + P(X = 12)$

=>$P(X \ge 10 ) = [ ^{12}C_{10} * (0.80)^{10} * (1- 0.80)^{12-10}] + [ ^{12}C_{11} * (0.80)^{11} * (1- 0.80)^{12-11}] + [ ^{12}C_{12} * (0.80)^{12} * (1- 0.80)^{12-12}]$    

=>$P(X \ge 10 ) = [ 66 * 0.1073 * 0.04] + [ 12 * 0.0859 * 0.2] + [1* 0.0687} * 1]$  

=>$P(X \ge 10 ) = 0.558$