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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.

پاسخ تشریحی :
نمایش پاسخ

a) $Po\left( {3.3} \right)$

${e^{ - 3.3}}(1 + 3.3 + \frac{{{{3.3}^2}}}{2})$

$ = 0.359$

b) $X\~Po\left( {36} \right)$

$X\~N\left( {36,{\text{ }}36} \right)$

$\frac{{48.5 - 36}}{{\sqrt {36} }}$

$ = 2.08\left( 3 \right)$

comp with 1.96

Evidence to support claim

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