Statistics Normal Distribution with Standard deviations

Question

Question 1: A manufacturer of ice pops fills each plastic container with a fruity liquid,
leaving enough room so that consumers can freeze the product. A filling machine is set so
that the amount of liquid in each ice pop is normally distributed with mean 8.00 ounces and
standard deviation 0.25 ounces. Suppose 16 ice pops are randomly selected.

 

What is the probability that the sample mean is more than 8.15 ounces.

 

Also. Suppose the filling machine operator can fine-tune the process by controlling the standard
deviation of the fill. Find a value of σ such that the probability that the sample
mean is more than 8.05 ounces is 0.05.

Answer 1

1) P(μ>8.15) = 1-P(μ<8.15) = 1-Φ((8.15-8)/.25/√16)) = 1 - Φ(2.4) = .0082

 

2) P(μ>8.05)=.05 = 1-P(μ<8.05) = .05

P(μ<8.05)=.95

((8.05-8)/σ/√16)=Φ(.95)

.05/(σ/4)=1.645

solve for σ:

σ=.121581