Question

1. The new Twinkle bulb has a standard deviation hours. A random sample of 60 light bulbs is selected from inventory. The sample mean was found to be 500 hours.

Construct 90%, 95% and 99% confidence intervals for the mean life,  of all Twinkle bulbs. Round to the nearest three decimals.

Please help me solve this with steps

Answer 1

Answer on Question #47127 – Math – Statistics and Probability

The new Twinkle bulb has a standard deviation hours. A random sample of 60 light bulbs is selected from inventory. The sample mean was found to be 500 hours.

Construct 90%, 95% and 99% confidence intervals for the mean life, ☐ of all Twinkle bulbs. Round to the nearest three decimals.

Solution.

To answer this question, we need to know the standard deviation $\sigma$.

Then the margin of error for 90% confidence interval will be:

$$1.645 \frac{\sigma}{\sqrt{60}} = 0.212\sigma;$$

the margin of error for 95% confidence interval will be:

$$1.96 \frac{\sigma}{\sqrt{60}} = 0.253\sigma;$$

the margin of error for 99% confidence interval will be:

$$2.58 \frac{\sigma}{\sqrt{60}} = 0.333\sigma;$$

And the confidence intervals for the mean life, respectively:

90%: (500 – 0.212σ, 500 + 0.212σ);

95%: (500 – 0.253σ, 500 + 0.253σ);

99%: (500 – 0.333σ, 500 + 0.333σ).

For example, for standard deviation $\sigma = 40$:

90%: (491.520, 508.480);

95%: (489.880, 510.120);

99%: (486.680, 513.320).

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