Answer:
95% confidence interval for the mean efficiency is [84.483 , 85.517].
Step-by-step explanation:
We are given that in a sample of 60 electric motors, the average efficiency (in percent) was 85 and the standard deviation was 2.
So, the pivotal quantity for 95% confidence interval for the population mean efficiency is given by;
P.Q. =
~ 
where,
= sample average efficiency = 85
= sample standard deviation = 2
n = sample of motors = 60
= population mean efficiency
<em>So, 95% confidence interval for the mean efficiency, </em>
<em> is ;</em>
P(-2.0009 <
< 2.0009) = 0.95
P(-2.0009 <
< 2.0009 ) = 0.95
P(
<
<
) = 0.95
P(
<
<
) = 0.95
<u>95% confidence interval for</u>
= [
,
]
= [
,
]
= [84.483 , 85.517]
Therefore, 95% confidence interval for the population mean efficiency is [84.483 , 85.517].