Question

The quality control manager at a light bulb manufacturing company needs to estimate the mean life of the light bulbs produced at the factory. The life of the bulbs is known to be normally distributed with a standard deviation (sigma) of 80 hours. A random sample of 16 light bulbs indicated a sample mean life of 1000 hours. What is a 95% confidence interval estimate (CIE) of the true mean life (m) of light bulbs produced in this factory

Answer 1

Answer: (960.80,1039.20)

Explanation:

Let X denotes a random variable that represents the life of the light bulbs produced at the factory.

As per given,

`\sigma=80\\\\ n=16\\\\ \overline{x}=1000`

Critical z-value for 95% confidence interval : z* = 1.96

Confidence interval for population mean:

`\overline{x}\pm z^*(\sigma)/(√(n))\\\\ =1000\pm (1.96)(80)/(√(16))\\\\=1000\pm 1.96*(80)/(4)\\\\=1000\pm 1.96*20\\\\=1000\pm39.2\\\\=(1000-39.2,\ 1000+39.2)\\\\=(960.80,1039.20)`

So, a 95% confidence interval estimate (CIE) of the true mean life (m) of light bulbs produced in this factory = (960.80,1039.20)