5 The number of adult customers arriving in a shop during a 5-minute period is modelled by a random variable with distribution \(\operatorname { Po } ( 6 )\). The number of child customers arriving in the same shop during a 10 -minute period is modelled by an independent random variable with distribution \(\mathrm { Po } ( 4.5 )\).

1. Find the probability that during a randomly chosen 2 -minute period, the total number of adult and child customers who arrive in the shop is less than 3 .
2. During a sale, the manager claims that more adult customers are arriving than usual. In a randomly selected 30 -minute period during the sale, 49 adult customers arrive. Test the manager's claim at the 2.5\% significance level.