7 The time Rafa spends on his homework each day in term-time has a normal distribution with mean 1.9 hours and standard deviation \(\sigma\) hours. On \(80 \%\) of these days he spends more than 1.35 hours on his homework.
- Find the value of \(\sigma\).
- Find the probability that, on a randomly chosen day in term-time, Rafa spends less than 2 hours on his homework.
- A random sample of 200 days in term-time is taken. Use an approximation to find the probability that the number of days on which Rafa spends more than 1.35 hours on his homework is between 163 and 173 inclusive.