Home / Expert Answers / Statistics and Probability / it-is-known-that-the-amount-of-time-needed-to-change-oil-in-a-car-is-normally-distributed-with-a-st-pa756

(Solved): It is known that the amount of time needed to change oil in a car is normally distributed with a st ...




It is known that the amount of time needed to change oil in a car is normally distributed with a standard deviation of 8 minu
It is known that the amount of time needed to change oil in a car is normally distributed with a standard deviation of 8 minutes. The amount of time to complete a random sample of 10 oil changes was recorded and listed as follows: a) Compute the confidence interval of the population mean. b) Compute the confidence interval of the population mean. c) Describe the effect on the confidence interval when decreasing the confidence level. (3) (1)


We have an Answer from Expert

View Expert Answer

Expert Answer



a) To compute the 99% confidence interval of the population mean, we can use the t-distribution since the sample size is small (n = 10) and the population standard deviation is unknown. The formula for the confidence interval is:
  
where X? is the sample mean, t is the critical value from the t-distribution for the desired confidence level and degrees of freedom (n-1), s is the sample standard deviation, and n is the sample size.
First, let's calculate the sample mean and sample standard deviation: Sample mean (X?) =  
Sample standard deviation (s) =   
Next, we need to find the critical value for the t-distribution with 9 degrees of freedom and a confidence level of 99%. Using a t-table or statistical software, we find the critical value to be approximately 3.250.
Now we can calculate the confidence interval: Confidence Interval =    Confidence Interval ?   

Therefore, the 99% confidence interval for the population mean is approximately   .


here we calculate the population mean.



We have an Answer from Expert

Buy This Answer $5

Place Order

We Provide Services Across The Globe