Answer :
Answer:
Probability = 0.1038 or 10.38%
Step-by-step explanation:
Given,
Number of sheets n = 250
Mean [tex]\mu =0.08[/tex]
Standard deviation [tex]\sigma =0.01[/tex]
[tex]S_{n}[/tex] = Sum of sample items.
From the Central Limit Theorem we get, [tex]S_{n}[/tex]~[tex]N(n\mu ,n\sigma^2)[/tex]
n\mu = 250 × 0.08
= 20
[tex]\sigma^2S_{n}=n\sigma^2[/tex]
= 250(0.01)²
= 0.025
Therefore, [tex]S_{n}[/tex]~N(20,0.025)
The Z-value corresponding to 20.2 :
[tex]Z=\frac{20.2-20}{\sqrt{0.025}}[/tex]
= 1.26
Finally, [tex]P(S_{n}>20.2)=P(z>1.26)[/tex]
= 1 - 0.8962
= 0.1038
Probability = 0.1038 or 10.38%