Question

Suppose a car manufacturer believes its windscreen wipers will last on average for three years on their cars if driven by a typical driver in the province. Moreover, the manufacturer believes the lifetime of the wipers under such conditions is Normally distributed with a standard deviation of two years. Find the probability that, if on a car driven by a typical driver, a windscreen wiper lasts for a time that is not within 1.7 years of the mean lifetime.
The probability is:?

Answer 1

You need to calculate the z-scores for (3.0 - 1.7) years and (3.0 + 1.7) years.
Then you use a standard normal distribution table to calculate the required probability.
The formula for finding the z-score is
\[z=\frac{X-\mu}{\sigma}\]