Chapter 7, Problem AP2.7CPT

To determine

To find: the minimum number of unbroken briquettes’ the bag would have to contain for the company to avoid having to replace the bag for free.

Answer to Problem AP2.7CPT

418

Explanation of Solution

Given:

  $\mu =450,\sigma =20$

Formula used:

  $Z=\frac{X-\mu }{\sigma }$

Calculation:

  $X~Normal\left(\mu =450,\sigma =20\right)$

  $Z~Normal\left(\mu =0,\sigma =1\right)$

  $P\left(Z<-1.645\right)=0.05;Z=-1.645$

The 5^th percentile can be calculated using the Z table from the book, look for 0.05 within the table, the associating Z value is which looking forth.

  $Z=\frac{X-\mu }{\sigma }$

  $X=\sigma \ast Z+\mu$

  $X=-1.645\ast 20+450=417.1$

Knowing that Z=-1.645

  $X=418$

Hence, the correct option is (c)