A course takes in exactly 10 students. On average, a student has p% chance of achieving a distinction.
Given that the probability 7 students scoring distinction is greater than the probability of any other number of students scoring distinction, find the possible range of values of p.
Solution
Since the question did not ask for exact values of p, we can use the GC to solve this question.
We are looking at where the blue graph is above the red and black graph.
Hence 63.6<p<72.7
Example 1
Solution
Enter the data in the GC as follows:
Variance can also calculated using the GC as follows:
Example 2
This challenging question on normal distribution was posted in Edusnap by a student.
There were two mistakes made:
1) Interpreting the distribution of 2 large hampers and n small hampers as 2L + nS.
2) Calculation of variance
Here is the correct solution:
Smallest possible value of n = 9
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When the question mentions n items, the distribution is X1+X2+…Xn. When the question asks for “n times of a randomly chosen..”, then the distribution is nX.
Students also need to be familiar with calculating the expectation and variance of the sum or difference of normal distribution using the formula:
JC A Level H2 Math Tuition Singapore 
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