Question

1. The life in hours of a 75-watt light bulb is known to be normally distributed with standard deviation of 16 hours. A random sample of 8 light bulbs are selected and the respective lifetime for each light bulb were recorded as follows: 1052 1029 1031 1047 1056 1042 1038 1065 i. Construct a 95% confidence interval on the true mean lifetime. ii. Determine the minimum sample size, if the 98% confidence interval is within 2.5 of the true mean lifetime.

Name: 1 the life in hours of a 75 watt light bulb is known to be normally distributed with standard deviation of 16 hours a random sample of 8 light bulbs are selected and the respective lifetime 46016
Uploaded: 2022-07-24T16:12:09-08:00
Duration: 3 min 15 s
Channel: Sheryl Ezze
Description: 1 the life in hours of a 75 watt light bulb is known to be normally distributed with standard deviation of 16 hours a random sample of 8 light bulbs are selected and the respective lifetime 46016

          1. The life in hours of a 75-watt light bulb is known to be normally distributed with standard deviation of 16 hours. A random sample of 8 light bulbs are selected and the respective lifetime for each light bulb were recorded as follows:
1052 1029 1031 1047 1056 1042 1038 1065
i. Construct a 95% confidence interval on the true mean lifetime.
ii. Determine the minimum sample size, if the 98% confidence interval is within 2.5 of the true mean lifetime.

1 the life in hours of a 75 watt light bulb is known to be normally distributed with standard deviation of 16 hours a random sample of 8 light bulbs are selected and the respective lifetime 46016

Added by Christopher K.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

07/24/2022

Step 1

The data is: 1052, 1029, 1031, 1047, 1056, 1042, 1038, 1065 $\bar{x} = \frac{1052 + 1029 + 1031 + 1047 + 1056 + 1042 + 1038 + 1065}{8} = 1042.5$ $s = \sqrt{\frac{\sum_{i=1}^{8}(x_i - \bar{x})^2}{8-1}} = \sqrt{\frac{(1052-1042.5)^2 + (1029-1042.5)^2 + ... + Show more…

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1. The life in hours of a 75-watt light bulb is known to be normally distributed with standard deviation of 16 hours. A random sample of 8 light bulbs are selected and the respective lifetime for each light bulb were recorded as follows: 1052 1029 1031 1047 1056 1042 1038 1065 i. Construct a 95% confidence interval on the true mean lifetime. ii. Determine the minimum sample size, if the 98% confidence interval is within 2.5 of the true mean lifetime.