Answer:
Part A: yes
Part B: 50%
Step-by-step explanation:
There are two ways we can use a normal approximation for a sample: if the population it is from is normally distributed, or if the sample is sufficiently large (n > 30). In this case, we don't know if the population is normally distributed, but we do know the sample size is larger than 30, so we can use normal approximation.
The sample proportion is normally distributed, with a mean equal to the mean of the population. So there is a 50% chance that sample proportion is less than the population proportion.
Answer:
1) For 
: 
and 
, 2) For 
: 
and 
Step-by-step explanation:
The polynomial 
is a second-order polynomial of the form 
. By direct comparison, we construct the following system of equations:
(1)
(2)
By (1) we know that there are a family of pairs such that the system of equations is satisfied. Let suppose that both 
and 
are integers. We assume two arbitrary integers for :
1)
2)
