Question

U fill containers with an average of 12 ounces of oil with

astanderd deviation of .25 ounces. take a random sample of 40
cans,what is the probability that the sample mean,X is grater
then12.05.

Answer 1

Answer: 0.1038

Explanation:

We assume that oil in each container is filled will normal distribution.

Given : Population mean :
`\mu=12`

Standard deviation:
`\sigma=0.25`

Sample size :
`n=40`

Let x be the random variable that denotes the amount of oil filled in container.

z-score :
`z=(x-\mu)/((\sigma)/(√(n)))`

For x= 12.05

`z=(12.05-12)/((0.25)/(√(40)))=1.26491106407\approx1.26`

Now by using the standard normal table for z, we have the probability that the sample mean,X is greater then 12.05:-

`P(z>1.26)=1-0.8961653=0.1038347\approx0.1038`

Hence, the probability that the sample mean,X is greater then 12.05 = 0.1038