Question

A chocolate factory produces mints that weigh 10 grams apiece. The standard deviation of the weight of a box of 10 mints is 3 grams. You buy a box of mints that weighs 95 grams. What is your confidence that the box you bought did not come from the factory?
90%
95%
10%
5%

Answer 1

The confidence that the box you bought did not come from the factory is 90 %.

Step-by-step explanation:

Since we have given that

Population Mean weight (\mu)= 10 grams a piece

Standard deviation of the weight of a box = 3 grams

Number of mints = 10

We need to buy a box of mints that weighs 95 grams.

Sample mean is given by

x = $\frac{95}{10}=9.5$ grams .

First we find out the standard error which is given by

$s=\frac{\sigma}{\sqrt{n}}\\\\=\frac{3}{\sqrt{10}}$= 0.94868

Since it is normal distribution, so, we will find z-score.

$z=\frac{x-\mu}{s}\\\\z=\frac{9.5-10}{0.94868}\\\\z=-0.527$

z = - 0.53

The area to the left of a z-score of -0.53 = 0.29805.

So, it may be 90% or 95 % confidence.

For 95% confidence level,

$\alpha=\frac{1-0.95}{2}=0.025$

Similarly,

For 90% confidence level,

$\alpha=\frac{1-0.90}{2}=0.05$

The value is much smaller than 0.05.  

So, we will get 90% confidence and the critical value = 1.645

Margin of error is given by

(Standard deviation) $\times$ (critical\ value) = 0.94868 $\times$ 1.645

                                                              =1.56

So, confidence interval will be

                          (10-1.56,10+1.56)

                              =(8.44,11.56)