Question

The foreman of a bottling plant has observed that the amount of soda in each \16-ounce" bottle is actually a normally distributed random variable, with a mean of 15.9 ounces and a standard deviation of 0.1 ounce. If a customer buys one bottle, what is the probability that the bottle will contain more than 16 ounces

Answer 1

Answer: 0.1587

Explanation:

Given : The foreman of a bottling plant has observed that the amount of soda in each 16-ounce bottle is actually a normally distributed random variable, with

`\mu=15.9\text{ ounces}`

Standard deviation :
`\sigma=0.1\text{ ounce}`

Let x be the amount of soda in a randomly selected bottle.

Z-score :
`(x-\mu)/(\sigma)`

`z=(16-15.9)/(0.1)=1`

The probability that the bottle will contain more than 16 ounces using standardized normal distribution table :

`P(x>16)=P(z>1)=1-P(z<1)\\\\=1-0.8413447=0.1586553\approx0.1587`

Hence, the probability that the bottle will contain more than 16 = 0.1587