Question

In: Statistics and Probability

Problem Page The lifetime of a certain brand of electric light bulb is known to have...

Problem Page

The lifetime of a certain brand of electric light bulb is known to have a standard deviation of

hours. Suppose that a random sample of

bulbs of this brand has a mean lifetime of

480

hours. Find a

99%

confidence interval for the true mean lifetime of all light bulbs of this brand. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

Solutions

Expert Solution

Solution :

Given that,

= 480

= 48

n = 50

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 2.576 * (48 / $\sqrt$ 50)

= 17.5

At 99% confidence interval estimate of the population mean is,

- E < < + E

480 - 17.5 < < 480 + 17.5

462.5 < < 497.5

(462.5 , 497.5)

orchestra answered 1 year ago

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