Electra is employed by E \& G Ltd to install electricity meters in new houses on an estate. Her time, \(X\) minutes, to install a meter may be assumed to be normally distributed with a mean of 48 and a standard deviation of 20 .
Determine:
\(\mathrm { P } ( X < 60 )\);
\(\mathrm { P } ( 30 < X < 60 )\);
the time, \(k\) minutes, such that \(\mathrm { P } ( X < k ) = 0.9\).
Gazali is employed by E \& G Ltd to install gas meters in the same new houses. His time, \(Y\) minutes, to install a meter has a mean of 37 and a standard deviation of 25 .
Explain why \(Y\) is unlikely to be normally distributed.
State why \(\bar { Y }\), the mean of a random sample of 35 gas meter installations, is likely to be approximately normally distributed.