Question

Potato chips Refer to Exercise $47$ About what percent of $9-$ounce bags of

this brand of potato chips weigh less than the advertised $9$ ounces? Is this likely to pose a problem for the company that produces these chips?

Short answer

Around $0.82$ percent of this brand's $9$ ounce bags of potato chips are less than the advertised $9$ ounces. For the firm that makes these chips, it is unlikely to be a problem.

Step-by-step solution

Given information

Bag weighs, $x=9$

Mean, $\mu =9.12$

Standard deviation, $\sigma =0.05$

Concept

The formula used: $z=\frac{x-\mu }{\sigma }$

Calculation

Calculate the $z-$score,

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

Use the normal probability table in the appendix to get the corresponding probability.

The usual normal probability table for $P(z<-2.40)$has a row that starts with $-2.4$and a column that starts with$.00$

$$\begin{gathered} P(x<9)=P(z<-2.40) \\ =0.0082 \\ =0.82\% \end{gathered}$$

As a result, approximately $0.82$percent of this brand's $9-$ounce bags of potato chips weigh less than the advertised $9$ounces. This signifies the occurrence of an exceptional event because the probability is less than $0.05$(or $5\%$). (or impossible event). As a result, the company that makes these chips is unlikely to face any difficulties.