1) A light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hours. A sample of 100 light bulbs from the company were tested and the researcher found that the average life of each light bulb was 1050 hours. At a 95% confidence level, determine whether these light bulbs are in compliance with the company's claim.

Question

Mathematics

Reece

30 August, 09:25

1) A light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hours. A sample of 100 light bulbs from the company were tested and the researcher found that the average life of each light bulb was 1050 hours. At a 95% confidence level, determine whether these light bulbs are in compliance with the company's claim.

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Mariana Montgomery · Answer 1

The mean (average) is given as 1200 hours.

The standard deviation is 200, sample size is 100.

Find the standard error:

√ (200^2 / 100) = 20

Now calculate the confidence interval. For 95% the Z number is 1.96

Multiply Z by the standard error:

1.96 x 20 = 39.2

Now find the range that the mean should be within:

1200 - 39.2 = 1160.8

1200 + 39.2 = 1239.2

The samples should be between 1160.8 and 1239.2 for a 95% confidence interval.

Since the average was 1050, which is below 1160.8 the bulbs are not in compliance.