In: Math
Solution:
Given that X follows a distribution with
= 40
= 18
A sample of size n = 38 is taken from this population.
Let be the sample mean.we know the distribution of is normal with
Mean = = = 40
SD = = = 18 /38 = 2.91998558 (It is called as the standard error of the mean)
Find P(sample mean time is 38 hours or less)
= P( 38)
= P[( - )/ (38 - )/ ]
= P[Z (38 - 40)/2.91998558 ]
= P[Z -0.6849 ]
= 0.2467 ...use Z table to find P[Z -0.6849 ]