Question

A simple random sample of electronic components will be selected to test for the mean lifetime in hours. Assume that component lifetimes are normally distributed with population standard deviation of 27 hours. How many components must be sampled so that a 99% confidence interval will have margin of error of 3 hours?

Answer 1

Answer:

540

Step-by-step explanation:

we have given E=0.3

σ = 27 hours

100(1-α)%=99%

from here α=0.01

using standard table $Z_\frac{\alpha }{2}=Z_\frac{0.01}{2}=2.58$

$n=\left ( Z_\frac{\alpha }{2}\times \frac{\sigma }{E} \right )^{2}$ =

$\left ( 2.58\times \frac{27}{3} \right )^{2}$

n = $23.22^{2}$

n=539.16

n can not be in fraction so n=540