4. The Department of Health recommends that adults aged 18 to 65 should take part in at least 150 minutes of aerobic exercise per week. The results of a survey show that 940 out of 2000 randomly selected adults aged 18 to 65 in Wales take part in at least 150 minutes of aerobic exercise per week.

1. Calculate an approximate \(95 \%\) confidence interval for the proportion of adults aged 18 to 65 in Wales who take part in at least 150 minutes of aerobic exercise per week.
2. Give two reasons why the interval is approximate.
3. Suppose that a \(99 \%\) confidence interval is required, and that the width of the interval is to be no greater than \(0 \cdot 04\). Estimate the minimum additional number of adults to be surveyed to satisfy this requirement.