1 Each month the amount of electricity, measured in kilowatt-hours ( kWh ), used by a particular household is Normally distributed with mean 406 and standard deviation 12.
- Find the probability that, in a randomly chosen month, less than 420 kWh is used.
The charge for electricity used is 14.6 pence per kWh .
- Write down the distribution of the total charge for the amount of electricity used in any one month. Hence find the probability that, in a randomly chosen month, the total charge is more than \(\pounds 60\).
- The household receives a bill every three months. Assume that successive months may be regarded as independent of each other.
Find the value of \(b\) such that the probability that a randomly chosen bill is less than \(\pounds b\) is 0.99 .
In a different household, the amount of electricity used per month was Normally distributed with mean 432 kWh . This household buys a new washing machine that is claimed to be cheaper to run than the old one. Over the next six months the amounts of electricity used, in kWh , are as follows.
$$\begin{array} { l l l l l l }
404 & 433 & 420 & 423 & 413 & 440
\end{array}$$
- Treating this as a random sample, carry out an appropriate test, with a \(5 \%\) significance level, to see if there is any evidence to suggest that the amount of electricity used per month by this household has decreased on average.