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
* ( 
/
= 2.05 * ( 40/
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)
orchestra answered 1 year agoRelated Solutions
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