Question 1181080
these questions can be answered with the use of the following normal distribution calculator.
<a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>
the mean is 30,000 and the standard deviation is 2000.


answers to each question are shown below:


a) What is the probability that a tire's lifespan is between 30,000 and 32,000 miles?


probability between 30,000 and 32,000 miles is .3413.


here's a display of the calculator results.


<img src = "http://theo.x10hosting.com/2021/052801.jpg">


b) What is the most number of miles that the bottom 10% of tires last?


most number of miles and still in the bottom 10% is equal to 27436.897.


here's a display of the results.


<img src = "http://theo.x10hosting.com/2021/052802.jpg">


c) What is the least number of miles that the top 5% of tires last?


least number of miles in the top 5% is equal to 33289.707.


here's a display of the results.


<img src = "http://theo.x10hosting.com/2021/052803.jpg">


d) Would it be unusual for a tire to last 35,000 miles? (Y/N


the probability of the tire lasting more than 35,000 miles is 0.0062.


that would be considered unlikely, since the probability is less than .01.
a probability of less than .01 means that more than 99% of the tires would have a life less than 35,000 miles.


here's a display of the results.


<img src = "http://theo.x10hosting.com/2021/052804.jpg">