A bakery claimed that the average number of loaves of bread sold per day is more than [latex]150[/latex], with variance [latex]2500[/latex]. A random sample of [latex]50[/latex]days was taken and the sales, [latex]x[/latex] loaves, for each day were recorded. It was found that
[latex]\sum{\left( x-140 \right)}=-120[/latex]
(i)
State, with a reason, whether it is necessary to assume that the bread sales follow a normal distribution in order to test this claim at the [latex]10\%[/latex] significance level.
(ii)
Test at the [latex]10\%[/latex] significance level whether the bakery’s claim was valid.