3 The random variable \(X\) represents the reaction times, in milliseconds, of men in a driving simulator. \(X\) is Normally distributed with mean 355 and standard deviation 52.

1. Find
   (A) \(\mathrm { P } ( X < 325 )\),
   (B) \(\mathrm { P } ( 300 < X < 400 )\).
2. Find the value of \(k\) for which \(\mathrm { P } ( X < k ) = 0.2\). It is thought that women may have a different mean reaction time from men. In order to test this, a random sample of 25 women is selected. The mean reaction time of these women in the driving simulator is 344 milliseconds. You may assume that women's reaction times are also Normally distributed with standard deviation 52 milliseconds. A hypothesis test is carried out to investigate whether women have a different mean reaction time from men.
3. Carry out the test at the \(5 \%\) significance level.