Question

5) In a simple random sample of 59 electronic components produced by a certain method, the mean lifetime was 1,114 hours. Assume the component lifetimes are normally distributed with population standard deviation 55 hours. What is the upper bound of the 95% confidence interval for the mean lifetime of the components? Round to nearest integer.

6) Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of 3 holes. In a sample of 83 clamps, the mean time to complete this step was 54.1 seconds. Assume the population standard deviation is 6 seconds. What is the lower bound of the 98% confidence interval? Round to one decimal place.

7)A sample of 200 1 year old baby boys had a mean weight of 25.4 lbs. Assume population standard deviation is 5.6 lbs. What is upper bound of the 90% confidence interval for mean lifetime of the components? Round to 2 decimal places.

8) A simple random sample of 10 households, number of TVs per household is: 1, 1, 3, 3, 2, 2, 3, 5, 0, 4 Population is approximately normal and population standard deviation is 0.42. What is lower bound of the 95% confidence interval for mean number of TVs? Round to 2 decimal places.

9) A college admissions officer takes a simple random sample of 99 entering freshman and computes their mean math SAT score to be 491. Population standard deviation is 117. What is lower bound of the 99% confidence interval? Round to nearest integer.

10) Simple random sample of 12 iphones had following price: 287, 311, 262, 392, 313, 265, 316, 286, 309, 276, 291 Population is approximately normal and population standard deviation is 71. What is upper bound of the 95% confidence interval for mean price of phones? Round to one decimal place.

11) Scientists want to estimate mean weight of mice after being fed special diet. Weight is normally distributed with standard deviation 3 grams. How many mice must be weighed so a 95% confidence interval will have margin error of 0.5 grams? Write only an integer as answer.

12) Simple random sample of electronics will be selected for test for mean lifetime in hours. Lifetimes are normally distributed with population standard deviation 16 hours. How many components must be sampled so a 99% confidence interval will have margin of error of 4 hours? Write only an integer as answer.

Answer 1

5) In a simple random sample of 59 electronic components produced by a certain method, the mean lifetime was 1,114 hours. Assume the component lifetimes are normally distributed with population standard deviation 55 hours. What is the upper bound of the 95% confidence interval for the mean lifetime of the components? Round to nearest integer.

Sample size = n = 59

Sample mean = = 1114

Population standard deviation = = 55

We have to find the upper bound of the 95% confidence interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 1.96 ( Using z table)

So confidence interval is ( 1114 - 14.0344 , 1114 + 14.0344) = > ( 1099.9656 , 1128.0344)

The upper bound = 1128

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