Question

the mean final examination scores for students taking SM2703 is 30 marks (out f 50 marks) with standard deviation of 6 marks. Assume that the final scores are approximately normal. Two random samples were taken randomly consisting of 32 and 50 students respectively. What is the probability that: a) The mean final examination scores will differ by more than 3 marks? b) Mean final examination scores from group 1 is larger than group 2? vv

Answer 1

Let define a random variable X that represent score of students taking SM2703.

The random variable X is normally distributed with mean 30 and standard deviation 6.

We take two random samples of size 32 and 50

Let the sample mean of first and second sample is denoted by

We know the linearity property of normal distribution.

i.e,

So, here

Now we will find the distribution of difference between two samples mean,

So, here

a) The mean final examination scores will differ by more than 3 marks?

Solution::

Here we need to find

[ for symmetricity of normal distribution]

The probability is 0.0272

b) Mean final examination scores from group 1 is larger than group 2?

Solution::

Here we need to find

[ from standard normal table we get]

The probability is 0.50