Step-by-step explanation:
hihi, so given a statistic, a sample standard deviation, and the sample size, we can create a 99% confidence interval for this distribution. Given the equations for confidence interval and Margin of Error, all we have to calculate initially is t* (invT(.995, 85-1)) and Standard error (34/sqrt(85)). Once we have these numbers, it's as easy as plugging in and doing some simple calculations to reaching our upper and lower fences of our interval. (136.28, 155.72). Any value below the lower fence or any value above the upper fence is not in our interval
The 99% confidence interval for the given random sample is between 136.5 and 155.5. The critical value for a 99% of confidence interval is 2.58.
The formula for the confidence interval is
C.I = μ ± Margin error
Where Margin error = critical value × Standard error and μ - mean
Standard error = δ/[tex]\sqrt{n}[/tex]
δ - standard deviation and n is the sample space.
The critical value (z) is obtained from the percentage confidence interval table.
Given that,
Sample space n = 85
Mean μ = 146 and δ = 34
Calculating the standard error:
S.E = δ/[tex]\sqrt{n}[/tex]
= 34/√85
= 3.68
The critical value for the 99% of the confidence interval is 2.58
Calculating the Margin error:
Margin error = 2.58 × 3.68
= 9.49
= 9.5
Then the 99% of the confidence interval is calculated as follows:
C.I = μ - Margin error (lower interval)
= 146 - 9.5
= 136.5
C.I = μ + Margin error (upper interval)
= 146 + 9.5
= 155.5
Thus, the 99% confidence interval is 136.5 - 155.5.
Learn more about confidence intervals here:
https://brainly.com/question/2396062
#SPJ2