Suppose that ice cream consumption per person at parties is normally distributed with a mean of 0.39 gallons, and a standard deviation of 0.26 gallons. If you are throwing a party with 33 guests, how much ice cream do you need to buy to make sure that the probability of having enough is 95%?
I am not sure how to work this problem. do I change the 95 % to .95 the subtract .39 and then .26/sqrt33. This is how I started and it is not correct the teacher said answer was 16 gals.
HINT:
I would say
$\mu_{33}=33\mu=12.87,\,\,\,\sigma^2_{33}=33\sigma^2\Rightarrow \sigma_{33}=\sqrt{33}\sigma=1.49$
Consumption of ice cream = X (random variable).
$P(X \le x) = F(x) = 0.95 \Rightarrow x = F^{-1}(0.95)$.
F (x) is the distribution function of the normal probability distribution $N(\mu_{33},\sigma^2_{33})$.