Chapter 2.2, Problem 53E

To determine

Percentage of 9 − ounce bags of this brand of potato chips weigh less than the advertised 9 ounces.

Whether it is likely to pose a problem for the company that produces these chips.

Answer to Problem 53E

Around 0.82% of the 9 − ounce bags of this brand of potato chips weigh less than the advertised 9 ounces.

It is not likely to pose a problem for the company that produces these chips.

Explanation of Solution

Given information:

Bag weighs, $x=9$

Mean, $\mu =9.12$

Standard deviation, $\sigma =0.05$

Calculations:

Calculate the z − score,

  $z=\frac{x-\mu }{\sigma }=\frac{9-9.12}{0.05}=-2.40$

Use normal probability table in the appendix, to find the corresponding probability.

See the row that starts with -2.4 and the column that starts with .00 of the standard normal probability table for $P\left(z<-2.40\right)$ .

  $\begin{array}{l}P\left(x<9\right)=P\left(z<-2.40\right)\\ =0.0082\\ =0.82\%\end{array}$

Thus,

Around 0.82% of the 9 − ounce bags of this brand of potato chips weigh less than the advertised 9 ounces.

Since the probability is less than 0.05(or 5%), this indicates the occurrence of unusual event (or impossible event). Therefore, it is not likely to pose a problem for the company that produces these chips.