7 The number of customer complaints received by a company per day is denoted by \(X\). Assume that \(X\) has the distribution \(\operatorname { Po } ( 2.2 )\).
- In a week of 5 working days, the probability there are at least \(n\) customer complaints is 0.146 correct to 3 significant figures. Use tables to find the value of \(n\).
- Use a suitable approximation to find the probability that in a period of 20 working days there are fewer than 38 customer complaints.
A week of 5 working days in which at least \(n\) customer complaints are received, where \(n\) is the value found in part (i), is called a 'bad' week.
- Use a suitable approximation to find the probability that, in 40 randomly chosen weeks, more than 7 are bad.