$(10\%)$ An existing make of car is known to break down on average one and a half times per

year $(=\frac{1\mathrm{.}5}{?}$ year$).$ A new model is introduced and the manufacturer claims that this model is

less likely to break down. Ten randomly selected cars break down a total of eight times within the

first year. That is$,$ the observed test statistic is $x=8.$ Calculate the $p-$value and test the

manufacturer's claim at a $5\%$ significance level.