Answer to Question #308695 in Statistics and Probability for Arthi

Question

Boxes of chocolates are produced with a mean weight of 510 g. Quality control checks show that 1 % of boxes are rejected because their weight is less than 485 g.

a Find the standard deviation of the weight of a box of chocolates.

b Hence find the proportion of boxes that weigh more than 525 g.

Answer 1

Mean $(\mu) =510g$

(a) $1\%$ has weight less than $485g$

Probability of having weight less than $485g$ $=0.01$

From the normal distribution tables

The Z score for p(0.01) $=-2.32$

$Z=\dfrac{X-\mu}{\sigma}$

$\sigma=\dfrac{X-\mu}{Z}=\dfrac{485-510}{-2.32}$

$\sigma=10.77$

(b) Probability that the box weighs more than $525g$

$Z=\dfrac{X-\mu}{\sigma}=\dfrac{525-510}{10.77}$

$Z=1.393$

Probability for $Z=1.393$

From normal distribution tables

$p(1.393)=0.91774$

Probability that the weight is more than 525g

$=1-0.91774=0.08226$

The proportion is $8.226\%$