Chapter 7, Problem 9PT

To determine

The correct answer about the interval in which 95% of the observations should occur from the options (a) 16.05 to 16.14 ounces, (b) $-0.30$ to $+0.30$ ounces, (c) 15.95 to 16.15 ounces, (d) 15.90 to 16.20 ounces, (e) None of the above.

Answer to Problem 9PT

The correct answer is (e).

Explanation of Solution

Given information:

Amount of bottles of shampoo to fill the machine = 16 ounces

Mean amount of shampoo = 16.05 ounces

Standard deviation = 0.1 ounce

Number of randomly selected bottles = 4

Consider that $n$ denotes the number of randomly selected bottles that is, $n=4$ ; $\sigma$ denotes the standard deviation that is, $\sigma =0.1$ and $\mu$ denotes the mean that is, $\mu =16.05$ .

In case of a Normal distribution, it is know that 95% of the observations lie within 2 standard deviations of the mean. But it is not given that the population distribution is normal so the central limit theorem cannot be applied.

Hence, the correct answer is (e).