Standard +0.3 This is a straightforward normal distribution problem requiring understanding of symmetry and use of standard tables. Students must recognize that P(3.2 < X < μ) = 0.475 implies 3.2 is positioned symmetrically below μ, then use inverse normal tables to find the z-score and solve for μ. It's slightly above average difficulty due to the need to interpret the probability statement correctly, but the calculation itself is routine once set up.
1 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 \(\mu\).
1 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 $\mu$.
\hfill \mbox{\textit{CAIE S1 2015 Q1 [4]}}