Question

Recall that the trash bag manufacturer has concluded that its new 30-gallon bag will be the strongest such bag on the market if its mean breaking strength is at least 50 pounds. In order to provide statistical evidence that the mean breaking strength of the new bag is at least 50 pounds, the manufacturer randomly selects a sample of n bags and calculates the mean _ x of the breaking strengths of these bags. If the sample mean so obtained is at least 50 pounds, this provides some evidence that the mean breaking strength of all new bags is at least 50 pounds. Suppose that (unknown to the manufacturer) the breaking strengths of the new 30-gallon bag are normally distributed with a mean of m 5 50.6 pounds and a standard deviation of s 5 1.62 pounds. a Find an interval containing 95.44 percent of all possible sample means if the sample size employed is

Answer 1

Complete Question

Recall that the trash bag manufacturer has concluded that its new 30-gallon bag will be the strongest such bag on the market if its mean breaking strength is at least 50 pounds. In order to provide statistical evidence that the mean breaking strength of the new bag is at least 50 pounds, the manufacturer randomly selects a sample of n bags and calculates the mean _ x of the breaking strengths of these bags. If the sample mean so obtained is at least 50 pounds, this provides some evidence that the mean breaking strength of all new bags is at least 50 pounds. Suppose that (unknown to the manufacturer) the breaking strengths of the new 30-gallon bag are normally distributed with a mean of m 5 50.6 pounds and a standard deviation of s 5 1.62 pounds. a Find an interval containing 95.44 percent of all possible sample means if the sample size employed is n=4

Answer:

`X=(48.98,52.22)`

Explanation:

From the question we are told that:

Sample Mean
`\mu=50.6`

`\sigma =1.62`

Sample size
`n=4`

Level of significance
`\alpha 100-95.4=>4.56`

Therefore

`Z-value( \alpha/2)=2`

Generally the equation for Interval is mathematically given by

`X=\mu \pm z(alpha/2)* (sd)/(sqrt(n))`

`X= 50.6 \pm z(0.0456/2)* (1.62)/(sqrt(4))`

`X=50.6 \pm 2*(1.62)/(2)`

`X=(48.98,52.22)`