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

Question

(-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???

Answer 1

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.