Question

A machine used for filling plastic bottles with a soft drink has a target mean fill volume of 2.9 liters and a known standard deviation of 0.05 liter.

State the sampling distribution of the sample mean, if you obtain a random sample of 25 bottles.

Options-

X bar ~ N(2.9, 0.01)

X ~ N(2.9, 0.01)

X ~ N(2.9, 0.05)

Answer 1

Solution :

Given that ,

mean = = 2.9

standard deviation = = 0.05

n = 25

sample distribution of sample mean is ,

=

= 2.9

sampling distribution of standard deviation

=  / n = 0.05 / 25=0.01

= 0.01

X bar ~ N(2.9, 0.01)

X bar ~ N(,2)