The probability that a car will last less than 10 years is 0.621%
We have given that,
Standard Deviation = A = 0.8
Mean = 12 years
We will use the normal distribution to calculate probability.
What is the probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Let a Random variable Z , has A = 0.8, and M= 12 years.
The probability that a car will be able to last < 10 years= P(Z<10)
\(=P[\frac{Z-M}{A} < \frac{10-12}{0.8}]\)
\(=P[\frac{Z-M}{A} < \frac{-5}{2}]\)
Pr (Z < -5/2) = 0.00621[ By using standard table]
= 0.00621 ×100
=0.621%
Therefore option A is correct.
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