The age distribution of students at a community college is given below.
Age (years) Number of students (f)
11)
Over 35 26
1103
A student from the community college is selected at random. Find the conditional probability that the student is at most 35 given that he or she is at least 26.
From the way you posted, I cannot understand your data. However….
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability for each Z score.
To find the conditional probability that the student is at most 35 given that he or she is at least 26, we need to use the formula for conditional probability:
P(A | B) = P(A ∩ B) / P(B),
where P(A | B) represents the probability of event A occurring given that event B has already occurred, P(A ∩ B) is the probability of both A and B occurring, and P(B) is the probability of event B occurring.
In this case, event A represents the student being at most 35 years old, and event B represents the student being at least 26 years old.
To find P(A ∩ B), the probability of the student being both at most 35 and at least 26, we first need to determine the total number of students in the given age range.
Looking at the age distribution, the number of students over 35 is given as 26. Therefore, the number of students at most 35 is the total number of students minus the number of students over 35:
Number of students at most 35 = Total number of students - Number of students over 35
= 1103 - 26
= 1077.
Now we have P(A ∩ B), the probability of the student being both at most 35 and at least 26.
Next, we need to calculate P(B), the probability of the student being at least 26. Since we're told that a student from the community college is selected at random, we can assume that each student has an equal chance of being selected.
Therefore, P(B) is the total number of students at least 26 divided by the total number of students:
P(B) = Number of students at least 26 / Total number of students
= 1103 / 1103
= 1.
Finally, using the conditional probability formula, we can find P(A | B):
P(A | B) = P(A ∩ B) / P(B)
= (1077 / 1103) / 1
= 1077 / 1103.
Thus, the conditional probability that the student is at most 35 given that he or she is at least 26 is 1077 / 1103.