1. H2 maths tips (9758) – Page 8 – JC A Level H2 Math Tuition Singapore

Distinguish X1+X2 from 2X

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:

Challenging Normal Distribution problem 3

Challenging Probability problem 5

An unbiased die is thrown 6 times. Calculate the probabilities that the six scores obtained will

i) be 1, 2,3, 4, 5,6 in some order

ii) have a product which is an even number

iii) consists of exactly two 6’s and four odd numbers

Solution

iii Alternative solution

6C2: 6 slots choose 2 slots to insert the two 6s. Remaining 4 slots automatically will be for the four odd numbers.
3^4: Each odd number has 3 choices. for 4 odd numbers will be 3^4

Probability = (6C2 x 3^4) / 6^6 = 5/192