Answer:
0.7143
- You know the minimum possible grade of the student
- You want to find out the probability that that grade which is greater than 72 is also greater than 84
- Expect the answer to be 0.7143
- The explanation/steps is given below
- The answer seems (and is) reasonable. You only created a new lower limit.
Step-by-step explanation:
Distribution Type: Normal
Mean: 78
Standard deviation: 36
Range of marks: [78 - 36], [78 + 36] = [42 to 114]
If you know that a student's grade is greater than 72, what is the probability that it's greater than 84?
In this case, the full probability level is between 72 and the upper limit of 114 (instead of between 42 and 114). First, find the fraction of this probability.
[114 - 72] ÷ [114 - 42] = 42/72 = 0.5833
So, the probability of a student's mark falling between 72 and 114 is 0.5833.
Now making this a whole interval, 114 - 72 = 42
What fraction of this interval of 42 will bear marks between 84 and 114?
[114 - 84] = 30
30/42 = 0.7143
Because of the first part of the question "If you know (are sure) that a student's grade is greater than 72...", your answer stops at 0.7143, since 72 was used as the lower limit.
and plug in the values for x and y.