Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
June 2015 p61 q1
3237
The lengths, in metres, of cars in a city are normally distributed with mean \(\mu\) and standard deviation 0.714. The probability that a randomly chosen car has a length more than 3.2 metres and less than \(\mu\) metres is 0.475. Find \(\mu\).
Solution
Given that the probability \(P(3.2 < X < \mu) = 0.475\), we can find the probability \(P(X < 3.2) = 0.5 - 0.475 = 0.025\).
Using the standard normal distribution table, \(P(Z < z) = 0.025\) corresponds to \(z = -1.96\).