Answer to Question #226868 in Statistics and Probability for rong

Question

The useful life of a certain type of light bulb is known to have a= 40 hours. Hoe large a sample should be taken standard deviation of it is desired to have a margin of error of 10 hours or less at a 95% level of confidence?

Answer 1

The required sample size can be calculated as,

$n=(\frac{(z×σ)}{ E})^2$

Where

z= is the critical value

σ= is the standard deviation

E=marginal error

Using the standard normal table, the critical value at the 95% confidence level is 1.96.

therefore

$n=(\frac{(z×σ)}{ E})^2\\=(\frac{(1.96×40)}{ 10})^2\\=61.46\\=62$