Question

Ink cartridges of a certain brand are labelled to indicate that they contain 12 ml.
Data has been collected about this brand. The corresponding sample statistics are n
= 36 and x̄ = 12.19 ml.
If the cartridges are filled so that μ = 12.00 ml (as labelled) and the population
standard deviation is σ = 0.11 ml (based on the observations), determine the
probability that a sample of 36 cartridges will have a mean of 12.19 ml or greater.
Discuss about your results.

NO EXCEL OR ANY OTHER STAT PACKAGE PLEASE

Answer 1

We are given X : cartridges are filled with mean = 12.00 ml and standard deviation = 0.11 ml

If n = 36 , we asked probability that a sample of 36 cartridges will have mean of 12.19 ml or greater

P( xbar 12.19) = P[(xbar -)/(/√n)(12.19-)/(/√n)]

P(xbar 12.19) = P( Z 10.83)

= 1 - P( Z < 10.83(

P(xbar 12.19) = 1 - 1

P(xbar 12.19) = 0.0000