Answer:
b. Normal with mean μ= -0.2 and standard deviation σ=0.1549
Step-by-step explanation:
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the real population proportion for Engineering
represent the estimated proportion for Engineering
is the sample size required for Engineering
represent the real population proportion for Humanities
represent the estimated proportion for Humanities
is the sample size required for Humanities
We assume that the population proportions follows a normal distribution since we satisfy these conditions:
,
The population proportion have the following distribution
And we are interested on the distribution for
For this case we know that the distribution for the differences of proportions is also normal and given by:
So then we can find the mean and the deviation like this:
So then the best option is :
b. Normal with mean μ= -0.2 and standard deviation σ=0.1549