5. The time taken for a randomly selected person to complete a test is \(M\) minutes, where \(M \sim \mathrm {~N} \left( 14 , \sigma ^ { 2 } \right)\)
Given that \(10 \%\) of people take less than 12 minutes to complete the test,
- find the value of \(\sigma\)
Graham selects 15 people at random.
- Find the probability that fewer than 2 of these people will take less than 12 minutes to complete the test.
Jovanna takes a random sample of \(n\) people.
Using a normal approximation, the probability that fewer than 9 of these \(n\) people will take less than 12 minutes to complete the test is 0.3085 to 4 decimal places.
- Find the value of \(n\).