The random variable $Y$ has a binomial distribution with mean 1.6 and $P\left( Y=0 \right)=0.1296$.

Question

The random variable $Y$ has a binomial distribution with mean 1.6 and $P\left( Y=0 \right)=0.1296$. Find $P\left( Y>2 \right)$. A car park has a large number of parking lots. $80$ parking lots are observed and the number of occupied parking lots is denoted by $X$. State, in context, two assumptions needed for $X$ to be well modelled by a binomial distribution. The probability of a parking lot being occupied is $0.95$. Using a suitable approximation, find the probability that out of $80$ chosen parking lots, at least $90\%$ are occupied.

Accepted Answer

$P(Y > 2) = 0.179$, $P(X \geq 72) = 0.982$

2013 MJC P2 Q8

2013 MJC P2 Q8

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