The number of adult customers arriving in a shop during a 5-minute period is modelled by a random variable with distribution $Po\left( 6 \right)$. The number of child customers arriving in the same shop during a 10-minute period is modelled by an independent random variable with distribution $Po\left( {4.5} \right)$.
a) Find the probability that during a randomly chosen 2-minute period, the total number of adultand child customers who arrive in the shop is less than 3.
b) 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.
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