Answer to Question #171930 in Statistics and Probability for Bikram Chaudhary

Question #171930

A manufacturing concern wants to estimate the average amount of purchase of its product in a month by the customers. If the standard deviation is Rs. 10, find the sample size, if the maximum error is not be exceed Rs. 3 with probability of 0.99.


1
Expert's answer
2021-03-17T10:57:11-0400

Let Xˉ=\bar{X}= the average amount of purchase: XˉN(μ,σ2/n).\bar{X}\sim N(\mu, \sigma^2/n).

The critical value for α=0.01\alpha=0.01 is zc=z1α/2=2.576.z_c=z_{1-\alpha/2}=2.576.

The corresponding confidence interval is computed as shown below:


CI=(Xˉzc×σn,Xˉ+zc×σn)CI=(\bar{X}-z_c\times\dfrac{\sigma}{\sqrt{n}}, \bar{X}+z_c\times\dfrac{\sigma}{\sqrt{n}})

Given σ=10\sigma=10


zc×σn3z_c\times\dfrac{\sigma}{\sqrt{n}}\leq3

n(zc×σ3)2n\geq(\dfrac{z_c\times\sigma}{3})^2

n(2.576×103)2n\geq(\dfrac{2.576\times10}{3})^2

n74n\geq74



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment