MATH SOLVE

3 months ago

Q:
# A researcher (Jack) comes to you and is interested in the average length of time a computer fan will run before it needs to be cleaned. Jack believes that this time period is approximately normally distributed with a standard deviation of 30 hours. You tell him to take a sample of computer fans. Jack comes back to you and says that he took a random sample of 36 computers, and found that the average length of time was 876 hours. Use a 94% confidence interval.

Accepted Solution

A:

Answer:94% confidence interval for the average length of time a computer fan will run before it needs to be cleaned is between 866.6 and 885.4 hoursStep-by-step explanation:94% confidence interval can be calculated using M±ME where M is the sample average length of time before it needs to be cleaned. (876 hours) ME is the margin of error from the mean margin of error (ME) around the mean using the formulaME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where z is the corresponding statistic in the 94% confidence level (1.88)s is the standard deviation of the time periods before it needs to be cleaned (30 hours)N is the sample size (36)Using the numbers we get ME=[tex]\frac{1.88*30}{\sqrt{36} }[/tex] =9.4Then the 94% confidence interval is 876±9.4