Please help stats exam questions

Hi
I have some stat questions, hope you can help as I have exam this mon, and have been trying to figure out the following questions.

Question 1
55% of all doctors recommend a new headache medicine.If we randomly select 15 doctors, and assume independence, find the probability of

1)At least 9 of them recommend the medicine
2)fewer than 9 of them recommend the medicine

I know I need to use the poission table, but I'm not sure about the values.

Question 2
If we wish to separate out the highest 20.05%, at what value would we draw the line?

Question3
If we randomly select 100 items from the original population, what is the probability the average below 1986 and above 1986?

Question 4
50% of the thousands of babies born in a 5-year period were boys. If we randomly select 900 babies,
1)what is the probability at least 439 were boys?
2)probability exactly 439 were boys
3)fewer than 439 were boys

Please advice. Thank you

Question 1
55% of all doctors recommend a new headache medicine.If we randomly select 15 doctors, and assume independence, find the probability of

Click to expand...

1)At least 9 of them recommend the medicine

Click to expand...

Binomial, not Poisson. \(\displaystyle {\mu}=np=15(.55)=8.25\)

\(\displaystyle {\sigma}=\sqrt{npq}=\sqrt{3.7125}\approx 1.927\)

Allow for continuity correction.

\(\displaystyle z=\frac{x-{\mu}}{\sigma}=\frac{8.5-8.25}{1.927}=.1297\)

Look this up in the z-table and subtract from 1. We subtract because it says "at least", so we want the area to the right of z=.1297

Question 2
If we wish to separate out the highest 20.05%, at what value would we draw the line?

Click to expand...

Look up .2005 in the body of the z-table and see what z-score corresponds. Then, using the above z formula, solve for x.

Question 2
If we wish to separate out the highest 20.05%, at what value would we draw the line?

Click to expand...

Look up .2005 in the body of the z-table and see what z-score corresponds. Then, using the above z formula, solve for x.[/quote]

Hi thank you so much but, may I know how do i know the mean and standard deviation for the above? I found the z = -8.4

Thanks again