The random variable $Y$ has a binomial distribution with mean $1.6$ and \(\mathrm{P}(Y=0)=0.1296

Question

The random variable $Y$ has a binomial distribution with mean $1.6$ and $\mathrm{P}(Y=0)=0.1296$. Find $\mathrm{P}(Y>2)$. 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 $0.95$. Find the probability that out of the $80$ chosen parking lots, at least $90$% are occupied.

Accepted Answer

(a) $0.1792$ (b) - The probability of a parking lot being occupied is constant throughout the $80$ parking lots. - Whether a parking lot is occupied is independent of whether any other parking lot is occupied.; $	ext{P}\left( X\ge 72 ight)=0.982$

2013 MJC P2 Q8 [Modified]

2013 MJC P2 Q8 [Modified]