The number 7

The number of faulty units in a carton of a particular product is known to be normally distributed with a Mean of 10 and a variance of 25. What portion of a given carton of the product is expected to contain___ faulty units?
(I) less than 8
(ii) more than 11
(iii) between 9 and 12

Correct answer:

a =  0.3446
b =  0.4207
c =  0.2347

Step-by-step explanation:

$$\begin{gathered} \mu =10 \\ r=25 \\ \sigma =\sqrt{r}=\sqrt{25}=5 \\ a=0.3446 \end{gathered}$$

Use the normal distribution table.

$b=0.4207$

Use the normal distribution table.

$$\begin{gathered} c=0.2347 \\ \text{ Verifying Solution: } \\ s=a+b+c=0.3446+0.4207+0.2347=1 \end{gathered}$$

Use the normal distribution table.

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