Khaleesi Herbert
2021-10-02
The standard deviation for a population is . This population's sample of 21 observations yielded a mean value of 139.05. It is well known that the population has a normal distribution.
Round your answers to two decimal places.
1) Make a confidence interval for . ( Enter your answer; confidence interval, lower bound ,Enter your answer; confidence interval, upper bound )
2) Construct a confidence interval for . ( Enter your answer; confidence interval, lower bound ,Enter your answer; confidence interval, upper bound )
3) Determine a confidence interval for . ( Enter your answer; confidence interval, lower bound ,Enter your answer; confidence interval, upper bound )
lobeflepnoumni
Skilled2021-10-03Added 99 answers
Step 1
Considering the data provided,
Population standard deviation
Sample size
Sample mean
1) Because we know the population standard deviation, we will use the z distribution.
The z value at confidence level from the standard normal table is 2.58.
The required confidence interval for µ can be obtained as:
Thus, the lower bound of confidence interval is and the upper bound is 147.38.
Step 2
2) The z value at confidence level from the standard normal table is 2.17.
The required confidence interval for can be obtained as:
Thus, the lower bound of confidence interval is 132.04 an the upper bound is 146.06
Step 3
3) The z value at confidence level from the standard normal table is 1.96.
The required confidence interval for can be obtained as:
As a result, the confidence interval's lower and upper bounds, respectively, are 132.72 and 145.38.
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