Explain why the bar for £10 000–£20 000 must have frequency density $0.0066$ (cars per £). Hence, state the scale of the vertical axis to $4$ d.p.

Let the frequency densities of the remaining classes, in order of increasing price, be $h_2$, $h_3$, $h_4$, $h_5$ (cars per £).
Write an expression for the total number of cars $N$ sold in the year in terms of $h_2$, $h_3$, $h_4$, $h_5$. State the class widths you used.

By reading the histogram carefully (use the tick marks and grid), estimate the heights $h_2$, $h_3$, $h_4$, $h_5$ to the nearest $0.0001$. Hence estimate the number of cars sold in each class and the total $N$.

Use your class frequencies to estimate the median price of a car sold. Use linear interpolation within the relevant class and show your working.

For price $p$ (in £) with $p \ge 10,000$, assume the frequency density $f(p)$ (cars per £) decays exponentially: $f(p)=A e^{kp}$, with $k<0$.
Using the point at the centre of the first full-width bar and the point at the centre of the final (long) bar (read these from the histogram), determine $A$ and $k$, giving each to $3$ s.f. Comment on the appropriateness of this model for the middle price classes.

A manager states: “At least $25$ of cars sold cost more than £40 000.”
Use your histogram-based calculations to assess this claim, giving a justified conclusion.