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

from the Z table, 95% are below 1.645 std above the mean

That means .39 + 1.645*.26 = .8177

So, there's a 95% chance that the average consumption is below .8177 gallons

For 33 people , that means that there's a 95% chance that .8177*33 = 26.98 gallons will fed them all.

Not sure how the answer is 16 gallons. Better check my math.

To determine how much ice cream to buy in order to ensure a 95% probability of having enough for all your guests, you can use the concept of a confidence interval.

First, let's find the z-score associated with the desired level of confidence. Since we want a 95% probability, the corresponding z-score can be found using a standard normal distribution table or a calculator.

For a 95% confidence interval, the z-score is approximately 1.96 (rounded to two decimal places).

Next, you'll need to calculate the margin of error. The margin of error is determined by multiplying the z-score by the standard deviation of the ice cream consumption per person and dividing it by the square root of the number of guests:

Margin of Error = z * (standard deviation / sqrt(number of guests))

In this case, the mean is 0.39 gallons, the standard deviation is 0.26 gallons, and the number of guests is 33.

Calculating the margin of error:

Margin of Error = 1.96 * (0.26 / sqrt(33)) ≈ 0.084 gallons

Finally, to determine the amount of ice cream needed, you'll add the margin of error to the mean:

Amount of Ice Cream Needed = mean + margin of error

Amount of Ice Cream Needed = 0.39 + 0.084 ≈ 0.474 gallons

So, according to this calculation, you would need to buy approximately 0.474 gallons (rounded to the nearest hundredth) of ice cream per person to ensure a 95% probability of having enough for all 33 guests at the party.

However, you mentioned that your teacher stated the answer is 16 gallons. It's possible that there may be some additional information or assumptions made by your teacher that differ from this calculation. It would be best to review the explanation with your teacher to understand their approach and reasoning for the different answer.