Draw a fully labelled tree diagram to illustrate the various choices that Sharik can make until the computer indicates that he has answered the question correctly.
The random variable \(X\) is the number of attempts that Sharik makes up to and including the one that the computer indicates is correct. Draw up the probability distribution table for \(X\) and find \(\mathrm { E } ( X )\).
(a) The time, \(X\) hours, for which people sleep in one night has a normal distribution with mean 7.15 hours and standard deviation 0.88 hours.
Find the probability that a randomly chosen person sleeps for less than 8 hours in a night.
Find the value of \(q\) such that \(\mathrm { P } ( X < q ) = 0.75\).
(b) The random variable \(Y\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\), where \(2 \sigma = 3 \mu\) and \(\mu \neq 0\). Find \(\mathrm { P } ( Y > 4 \mu )\).