Question

For a new type of tire, a racing car team found the average distance a set of tires would run during a race is 161 miles, with a standard deviation of 14 miles. Assume that tire mileage of each set is independent and follows a Normal model Give answers in decimal form rounded to four decimal places as needed. 1 If the team plans to change tires twice during a 500-mile race, what is the expected value and standard deviation of miles of use for the three sets of tires? A. The expected value for miles of use of the three sets of tires is Џ miles. B. The standard deviation for miles of use of the three sets of tires is miles 2. What is the probability they will have to change tires a third time before the end of a 500 mile race The probability they wil have to change tires a third time is

Answer 1

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Normal distribution params are given below:

Mean of race = 161 miles
Stdev of race = 14 miles

1.

A. Expected value = E(3X) =3*E(X) = 3*161 = 483 miles
B. Stdev of the 3 sets of tires = sqrt(Var(3X)0 = sqrt(9*Var(X)) = 3*sqrt(Var(X)) = 3*Stdev(X) = 3*14 = 42 miles

2.

We will use the normal params to standardize the distribution:

Prob that 3rd tires are change t0 before 500 miles
= P(X<500)
= P(Z< (500-E(3X))/STDEV(3X))
= P(Z< (500-483)/42)
= P(Z<.405)
= .6572

So, this is the probability