- Xian rolls a fair die 10 times.
The random variable \(X\) represents the number of times the die lands on a six.
- Using a suitable distribution for \(X\), find
- \(\mathrm { P } ( X = 3 )\)
- \(\mathrm { P } ( X < 3 )\)
Xian repeats this experiment each day for 60 days and records the number of days when \(X = 3\)
- Find the probability that there were at least 12 days when \(X = 3\)
- Find an estimate for the total number of sixes that Xian will roll during these 60 days.
- Use a normal approximation to estimate the probability that Xian rolls a total of more than 95 sixes during these 60 days.