If the population variance of the lifetime of a light bulb is 10000 hours, how large of a sample must be taken in order to be 99% confident that the margin of error will not exceed 35 hours

The sample must be greater than 55

Step-by-step explanation:

Confidence = 99% = 0.99

α = 1 - C = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

The z score of α/2 (0.005) corresponds to the z score of 0.495 (0.5 - 0.005) which is equal to 2.576

The margin of error (E) is given by the formula:

n > 55

The sample must be greater than 55 so that the margin of error will not exceed 35 hours

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

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