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brilliants [131]
3 years ago
11

Help me solve this problem 12.

Mathematics
1 answer:
photoshop1234 [79]3 years ago
8 0

the midpoint is (-3,2)    

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Answer:

The 95% confidence interval estimate for the population mean force is (1691, 1755).

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally.

The sample selected here is <em>n</em> = 30.

Thus, the sampling distribution of the sample mean will be normal.

Compute the sample mean and standard deviation as follows:

\bar x=\frac{1}{n}\sum x=\frac{1}{30}\times 51702=1723.4\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{30-1}\times 232561.2}=89.55

Construct a 95% confidence interval estimate for the population mean force as follows:

CI=\bar x\pm z_{\alpha /2}\times\frac{s}{\sqrt{n}}

    =1723.4\pm 1.96\times\frac{89.55}{\sqrt{30}}\\\\=1723.4\pm 32.045\\\\=(1691.355, 1755.445)\\\\\approx (1691, 1755)

Thus, the 95% confidence interval estimate for the population mean force is (1691, 1755).

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