MATH SOLVE

3 months ago

Q:
# A quality engineer in a light bulb factory is planning a study to estimate the average life of a large shipment of light bulbs. 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, determine the sample size for this study

Accepted Solution

A:

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.