Question

A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 1515 years with a variance of 2525. If the claim is true, in a sample of 4141 wall clocks, what is the probability that the mean clock life would differ from the population mean by more than 0.40.4 years

Answer 1

The correct answer will be "0.3043".

Explanation:

The given values are:

`\mu = 15`

`n=41`

`\sigma^2=25`

then,

`\sigma=5`

If researchers know representative sample n > 30 and default deviation those who use z-test

∴
`P(x>15.4)`

⇒
`1-P(x<15.4)`

⇒
`1-P((x-\mu)/((\sigma)/(√(n) ) ) <(15.4-15)/((5)/(√(41) ) ) )`

⇒
`1-P(Z<0.51225)`

⇒
`1-0.695762`

⇒
`0.3043`