In: Statistics and Probability
When a machine is properly calibrated, it takes an average time of 19.0 seconds to produce a widget, with a standard deviation of 2.8 seconds. For a simple random sample of n = 36 widgets, the sample mean production time is found to be x-bar = 20.2 seconds.
Solution :
Given that,
mean =
= 19.0
standard deviation =
= 2.8
n = 36
= 19.0
=
/
n = 2.8 /
36 = 0.467
P(
> 20.2 ) = 1 - P(
< 20.2 )
= 1 - P[(
-
) /
< ( 20.2 - 19.0) / 0.467]
= 1 - P(z < 2.57)
Using z table,
= 1 - 0.9949
= 0.0051
Probability = 0.0051