The service life X of a car tire has a Normal probability distribution with µ =...

The service life X of a car tire has a Normal probability distribution with µ = 50,000 miles and σ = 5500 miles. What is the probability that the useful life of a tire is greater than 3500 miles but less than 60,000 miles?

Expert Solution

Here in this Question it is given that the life of x car tires has mean 50000 and Standerd deviation is 5500.

Then we have to calculate the probability that the useful life of a car tires has life time in between 3500 and 60000 miles.

Here to calculate the above probability we have to use normal distribution method,

The standard z value is Z1= X1−μ/σ.

Using this method we calculated the probability as below,

Note that the probability value is calculated using the standard normal z-table or using Statistical software like excel.

The probability that the useful life of a tire is greater than 3500 mile but less than 60,000 mile is 0.9655.

The above shaded area represents the probability that the car tires has life time between 3500 miles and 60000 mile.

Hope it helps.

Thank you.

orchestra answered 2 years ago

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