Answer:
The required sample size is 171.
Step-by-step explanation:
Consider the provided information.
The engineer wants to estimate the average life within plus or minus 15 hours with 95 percent confidence. Assuming a process standard deviation of 100 hours,
First calculate the value of [tex]Z_{\frac{\alpha}{2}}[/tex]
By using the table we get.
[tex]Z_{\frac{\alpha}{2}}=1.96[/tex]
Now use the formula: [tex]N=(\frac{Z_{\frac{\alpha}{2}}\times \sigma}{E})^2[/tex]
Substitute the respective values in the above formula we get.
[tex]N=(\frac{1.96\times 100}{15})^2[/tex]
[tex]N=(\frac{1.96\times 100}{15})^2[/tex]
[tex]N=(\frac{196}{15})^2=170.73777[/tex]
[tex]N\approx171[/tex]
Hence, the required sample size is 171.