Answer:
Step-by-step explanation:
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 = 7900 miles
s = 5000 miles
A) We want to find the probability probability that the tyre wears out before 70000 miles. It is expressed as
P(x lesser than 70000)
For x = 70000,
z = (70000 - 79000)/5000 = - 1.8
Looking at the normal distribution table, the corresponding z score is 0.03593
B)We want to find the probability 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 - 79000)/5000 = 0.8
Looking at the normal distribution table, the corresponding z score is 0.78814
P(x greater than 83000)
= 1 - 0.78814 = 0.21
