7 The shortest time recorded by an athlete in a 400 m race is called their personal best (PB). The PBs of the athletes in a large athletics club are normally distributed with mean 49.2 seconds and standard deviation 2.8 seconds.
- Find the probability that a randomly chosen athlete from this club has a PB between 46 and 53 seconds.
- It is found that \(92 \%\) of athletes from this club have PBs of more than \(t\) seconds. Find the value of \(t\).
Three athletes from the club are chosen at random. - Find the probability that exactly 2 have PBs of less than 46 seconds.
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