SOLUTION: The lifespan of tires is normally distributed with a mean of 30,000 miles and a standard deviation of 2,000 miles. a) What is the probability that a tire's lifespan is between

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Question 1181080: The lifespan of tires is normally distributed with a mean of 30,000 miles and a standard deviation of 2,000 miles.
a) What is the probability that a tire's lifespan is between 30,000 and 32,000 miles?
b) What is the most number of miles that the bottom 10% of tires last?
c) What is the least number of miles that the top 5% of tires last?
d) Would it be unusual for a tire to last 35,000 miles? (Y/N
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
these questions can be answered with the use of the following normal distribution calculator.
https://davidmlane.com/hyperstat/z_table.html
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.

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.

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.

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.