Answer:
Step-by-step explanation:
Given
Mean = 4.68
Standard Deviation (SD) = 2.83
Value, x = 9.38
Required
Determine the z score
z score is calculated using the following formula;
Substitute 9.38 for x; 2.83 for SD and 4.68 for Mean
(Approximated)
<em>Hence, the z score is 1.66</em>
Using the binomial distribution, it is found that there is a 0.7941 = 79.41% probability that at least one of them is named Joe.
For each student, there are only two possible outcomes, either they are named Joe, or they are not. The probability of a student being named Joe is independent of any other student, hence, the <em>binomial distribution</em> is used to solve this question.
<h3>Binomial probability distribution </h3>
The parameters are:
In this problem:
The probability that at least one of them is named Joe is:
In which:
Then:
0.7941 = 79.41% probability that at least one of them is named Joe.
To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377