Solving Percentile Question: Find Canoe Carrying Capacity

[needhelp83]

I am not exactly sure what I am supposed to do to solve this problem:

The weight of people in a certain pacific island is normally distributed with a mean of 175 lb and a standard deviation of 33 lb. They want to design a one person canoe that will be able to serve 85% of the island's people. What should be the carrying capacity of the canoe?

Ok I know I wouldn't use a CI to solve this problem, but I am not sure what the exact setup would be. I have a hunch that I would use the percentiles where the Z critical value would be 1.04 using Z 15.

Where do I go from there?

 

[VeeEight]

Use the percent given to find the corresponding z score. You have population mean & standard deviation, as well as the z score, so you can solve for the unknown

 

[needhelp83]

Ok...

$$z= \frac{(x-\mu)}{\sigma}$$

$$1.04= \frac{(x- 175)}{33}$$

x = 209.32

This doesn't sound right to me at all with the s.d. and mean?

 

[Math Is Hard]

It looks right to me because if you were to go only one standard deviation up (z = 1), the x score would be 175 (M) + 33 (1 standard dev) = 208. At the 85th percentile, your z score (1.04) is just a little bit higher than that.