SOLUTION: A study of peach trees found that the average number of peaches per tree was 925. The standard deviation of the population is 35 peaches per tree. A scientist wishes to find the

Click here to see ALL problems on Probability-and-statistics

Question 727230: A study of peach trees found that the average number of peaches per tree was 925. The standard deviation of the population is 35 peaches per tree. A scientist wishes to find the 80% confidence interval for the mean number of peaches per tree. How many trees does she need to sample to obtain an average accurate to within 10 peaches per tree?
A) 13 B) 9 C) 14 D) 21

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
The standard deviation of the population is known (35), so we use the standard normal distribution.

So we use an inverse normal table to find the value of k that satisfies the equation

P(k < Z < k) = 0.8

or the equation

P(Z < -k) = 0.1

depending how your inverse normal table is set up

In any event, you will get k = 1.28155

So the critical z value (sometimes called z*) is z = 1.28155

-------------------------------------------------------

Variables Used
n = sample size
E = Margin of Error
sigma = population standard deviation
z = critical value

n = ( (z*sigma)/E )^2

n = ( (1.28155*35)/10 )^2

n = ( (44.85425)/10 )^2

n = ( 4.485425 )^2

n = 20.119037430625

n = 21 (remember to round UP to the nearest integer, this is so you are guaranteed clearance of the margin of error...basically you'll know that the margin of error is less than 10)

Min Sample Size: n = 21

So the answer is D) 21