It is claimed that the heights of a particular age group of boys follow a normal distribution with mean 125 cm and standard deviation 12 cm . Observations for a randomly chosen group of 60 boys in this age group are summarised in the following table. The table also gives the expected frequencies, correct to 2 decimal places, based on the normal distribution with mean 125 cm and standard deviation 12 cm .
(a) Show how the expected frequency for \(130 \leqslant x\lt 140\) is obtained.

(b) Carry out a goodness of fit test, at the \(5 \%\) significance level, to determine whether the claim is supported by the data.