SOLUTION: Find the probabilities. 1. The average life of a brand of automobile tires is 30 000 miles, with a standard deviation of 2000 miles. If a tire is selected and tested, find the pro

Question 1098403: Find the probabilities.
1. The average life of a brand of automobile tires is 30 000 miles, with a standard deviation of 2000 miles. If a tire is selected and tested, find the probability that it will have the following lifetime. Assume the variable is normally distributed.
a) between 25 000 and 29 000 miles
b) between 28 000 and 31 000 miles
c) between 32 500 and 34 500 miles
Please help me answer this.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd, mean is 30000, sd is 2000
z=(25000-30000)/2000=-2.5
(29000-30000)/2=-0.5
want z between -0.5 and -2.5, and from the calculator or table is 0.3023
for b
(-2000/2000)=-1 and (1000/2000)/2000=+0.5, and probability is 0.5328
for c
this is 2500/2000=+1.25 and 4500/2000=+2.5 and probability is 0.0317

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