A) The probability that the tyre wears out before 60000 miles is 0.4221
B) The probability that the tyre lasts more than 83000 miles is 0.49534
The distance the tyres can run until wear-out is a normally distributed, the formula for normal distribution is expressed as
z = (x - u)/s
Where
x = the distance the tyres can run until wear-out
u = mean distance
s = standard deviation
From the information given,
u = 70000 miles
s = 7000 miles
A) We want to find the Probability that the tyre wears out before 60000 miles. It is expressed as
P(x lesser than 60000)
For x = 60000,
z = (60000 - 70000)/7000 = - 1.42
Looking at the normal distribution table, the corresponding z score is 0.4221
B)We want to find the probability that the tyre lasts more than 83000 miles. It is expressed as
P(x greater than 83000) = 1 - P(x lesser than or equal to 83000)
For x = 83000,
z = (83000 - 70000)/5000 = 2.6
Looking at the normal distribution table, the corresponding z score is 0.49534
P(x greater than 83000)
= 1 - 0.49534 = 0.50466
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