If %1 of a popualtion are allergic to peanuts, would it be unusual for a random sample of n=1500 to result in fewer than 10 with peanut allergies? I have figured phat p=10/1500
(-0.007-0.01)/.003=-1
Z-score=-1=.1587
so Iinterpreted this to be 16 samples out of 100 will result in a sample proportion of .007 or less from the population whose proportion is .001, however am unsure if this is considered unusual or not???
Using the normal approximation to the binomial distribution, let's look at the information given to you in the problem.
Your values are the following:
p = .01, q = 1 - p = .99, x = 10, and n = 1500
We need to find mean and standard deviation.
mean = np = (1500)(.01) = 15
sd = √npq = √(1500)(.01)(.99) = 3.85
Now use z-scores:
z = (x - mean)/sd
With the above data:
z = (10 - 15)/(3.85) = ?
I'll let you finish the calculation. Determine the probability using a z-table. Remember the question is asking "fewer than 10" so you need to keep that in mind when looking at the table.
I hope this will help get you started.