Three Maths Problems

Question 1

It is believed that 10.7% of a group feels a certain way. To test this hypothesis at E=2% with a 90% confidence at least how many people were surveyed or what sample size is needed?

Question 2
It’s believed that 67% of people in America prefer purple Easter eggs.  A survey was done to test the hypothesis. A simple sample of size n=50 is obtained from the population.

Describe the sample distribution of P^. Is it approximately normal or not?
Find the backwards u sign sub p, and find the (it looks like the standard deviation sign sub p.)
If 39 out of 50 liked the purple eggs, compute the proportion, fraction, which like purple eggs and the z value corresponding to that proportion.
Assuming n-5- what is the probability of obtaining x=39 or more individuals with the characteristic?
Find a confidence interval for the value in part d value at the 96% level.

Question 3
A simple random sample of size n is drawn from a population that is normally distributed.  The sample mean, is found to be 40 and the sample standard deviation is found to be 7.
Construct a 96% confidence interval for sample mean if the sample size is Show your equation or calculator keys.