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babymother [125]
3 years ago
9

Construct a​ 95% confidence interval for the population standard deviation sigma of a random sample of 15 crates which have a me

an weight of 165.2 pounds and a standard deviation of 12.4 pounds. Round to the nearest thousandth. Assume the population is normally distributed.
Mathematics
1 answer:
Ad libitum [116K]3 years ago
4 0

Answer:

There is a 95% confidence that the sample has a mean between 158.92 pounds and 171.48 pounds

Step-by-step explanation:

Given that mean (μ) = 165.2 pounds, standard deviation (σ) = 12.4 pounds, sample size (n) = 15 crates. Confidence (C) = 95% = 0.95

α = 1 - C = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

The z score of α/2 corresponds to the z score of 0.475 (0.5 - 0.025) which is 1.96. z_{\frac{\alpha}{2} }=1.96

The margin of error (E) is given by:

E=z_{\frac{\alpha}{2} }\frac{\sigma}{\sqrt{n} } =1.96*\frac{12.4}{\sqrt{15} }= 6.28

The confidence interval = μ ± E = 165.2 ± 6.28 = (158.92, 171.48)

The confidence interval is between 158.92 pounds and 171.48 pounds. There is a 95% confidence that the sample has a mean between 158.92 pounds and 171.48 pounds

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Answer:

A. 8.3

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Step-by-step explanation:

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4 years ago
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Answer:

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Step-by-step explanation:

Hi, to answer this question we have to calculate the volume of a sphere:

Volume of a sphere: 4/3 π r³

Since diameter (d) = 2 radius (r)

Replacing with the value given:

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V = 4/3 π r³

V =4/3 π (17)³

V = 20,579.52 cubic inches

The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.

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To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=10,289.76

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