Question

In: Statistics and Probability

An electrical firm manufactures light bulbs that have a length of life that is approximately normally...

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has a an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = =

Population standard deviation =    =

Sample size = n =

At 96% confidence level the z is ,

= 1 - 96% = 1 - 0.96 = 0.04

/ 2 = 0.04 / 2 = 0.02

Z/2 = Z0.02= 2.05 ( Using z table )


Margin of error = E = Z/2 * ( /n)

= 2.05 * ( 40/   30)

E= 14.9711
At 96% confidence interval estimate of the population mean
is,

- E < < + E

780 - 14.9711 <   < 780 + 14.9711

765.0289 <   < 794.9711

( 765.0289 ,794.9711)


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