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The confidence that the box you bought did not come from the factory is 90 %.
<u>Step-by-step explanation:</u>
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 = grams
.
First we find out the standard error which is given by
= 0.94868
Since it is normal distribution, so, we will find z-score.
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,
Similarly,
For 90% confidence level,
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) (critical\ value) = 0.94868
1.645
=1.56
So, confidence interval will be
(10-1.56,10+1.56)
=(8.44,11.56)