Question

In post-apocalyptic Neverland, clean water is sold in "2-liter" bottles off the back of a truck that arrives every day. The arrival time is normally distributed with mean 2:54 pm and standard deviation 24 minutes. The time it takes for the water to sell out is also normally distributed with mean 33 minutes and standard deviation 7 minutes. The price of a "2-liter" bottle fluctuates from day to day according to a Normal distribution with mean 128 rubles and standard deviation 4 rubles. The amount of water in a "2-liter" bottle varies from bottle to bottle according to a Normal distribution with mean 63.5 ounces and standard deviation 1 ounce. Assume that all days, all times, and all bottles are independent.
On April 3, 2020, you buy four "2-liter" bottles of clean water. What is the probability that it costs you more than 500 rubles? Give your answer to 4 decimal places.

Answer 1

Answer:

0.7734

Step-by-step explanation:

The average in this problem is 128 and the standard deviation is 4.

We buy 4 bottles.  We want the probability that the cost is more than 500 rubles; this means the average of each bottle would be

500/4 = 125 rubles.  This is our X value.

Using the z score formula, we have

$z=\frac{X-\mu}{\sigma}\\\\=\frac{125-128}{4}=\frac{-3}{4}=-0.75$

Using a z table, the area under the curve less than this is 0.2266.  We want the probability that the cost is more than this, which would be to the right; we subtract from 1:

1-0.2266 = 0.7734