Mathematics, 30.05.2020 20:57 anikakurup0

The operations manager at a compact fluorescent light bulb (CFL) factory needs to estimate the mean life of a large shipment of CFLs. The manufacturer’s specifications are that the population standard deviation is 1,000 hours. A random sample of 64 CFLs indicated a sample mean life of 7,500 hours.

Construct a 95% confidence interval estimate for the popu- lation mean life of compact fluorescent light bulbs in this shipment.

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The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of 1-0.025 = 0.975 , so z = 1.95

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96*\frac{1000}{\sqrt{64}} = 245$

The lower end of the interval is the sample mean subtracted by M. So it is 7500 - 245 = 7255 hours.

The upper end of the interval is the sample mean added to M. So it is 7500 + 245 = 7745 hours.

The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.

Answer from: Quest

None of them would be estimated to be 3.5.

Answer from: Quest

1. which statement below is true for hyperbolic geometry?

answer: d

the sum of the measures of the angles in a triangle is always less than 180 degrees.

2. identify the statement that is true in spherical geometry.

answer: d

the sum of the measures of the angles of a triangle is greater than 180.

3. what can be said about the vertices of an equilateral triangle drawn in poincaré’s system?

answer: b

the vertices are equidistant from the center of the circle.

4. satellites sputnik, yeltsin, and plekov often temporarily line up in order in a great circle. the circumference of the earth is 24,900 miles, and the satellites orbit at about 150 miles above the surface. if, while in a great circle, sputnik is 9,000 miles from yeltsin, and yeltsin is 10,500 miles from plekov, how far apart are sputnik and plekov?

answer: b

6,342 miles

5. identify the statement that is true in spherical geometry.

answer: d

two distinct lines intersect in two points.

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