Respuesta :
Answer:
Step-by-step explanation:
Given that data from students doing a lab exercise are as follows:
33,190 31,860 32,590 26,520 33,280 32,320 33,020 32,030 30,460 32,700 23,040 30,930 32,720 33,650 32,340 24,050 30,170 31,300 28,730 31,920
Mean = 30841
Since normal and also sigma is known, std error
=[tex]\frac{\sigma}{\sqrt{n} } \\=\frac{3000}{\sqrt{40} } \\=474.34[/tex]
For95% margin of error = ±1.96(474.34) =±929.71
Hence 95% conf interval = 30841±929.71
=(29911.29, 31770.71)
The confidence interval for the mean load required to pull the wood apart is (29,485.192 , 32,114.8).
Given to us
Data set = {33190, 31860 32590 26520 33280 32320 33020 32030 30460 32700 23040 30930 32720 33650 32340 24050 30170 31300 28730 31920}
The standard deviation of the Normal distribution, s = 3000 pounds
confidence interval = 95%
Number of observations, n = 20
What is the mean of the given normal distribution?
To find the mean of the given interval of data,
[tex]Mean = \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}[/tex]
Mean, μ = 30,800
What is the margin of error?
We know the formula for the margin of error,
[tex]\text{MOE}_{\gamma}=z_{\gamma} \times \sqrt{\frac{s^{2}}{n}}[/tex]
Substitute the values,
[tex]\text{MOE}_{\gamma}=z_{\gamma} \times \sqrt{\frac{ 3000^{2}}{20}}[/tex]
[tex]\text{MOE}_{\gamma}= \pm 1,314.8079[/tex]
What is the confidence interval?
The confidence interval can be found out using,
Confidence interval = Mean ± MOE
= 30,800 ± 1,314.8079
= 29,485.192 , 32,114.8
Hence, the confidence interval for the mean load required to pull the wood apart is (29,485.192 , 32,114.8).
Learn more about Confidence intervals:
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