Question

a certain airline has a 90% probability that its flights are on time. fifteen of this airlines flights leave the local airport each day. let x represent the number of flights that are on time each day. assuming flights are on time independently of one another, what is the shape of the probability histogram of x?
o skewed left
skewed right
o approximately uniform
o approximately symmetric

Explanation:

For a binomial distribution \(X\sim B(n,p)\) (here \(n = 15\) flights, \(p=0.9\) probability of on - time flight). The mean of a binomial distribution is \(\mu=np\) and the standard deviation is \(\sigma=\sqrt{np(1 - p)}\).

The mean \(\mu=np=15\times0.9 = 13.5\). The standard deviation \(\sigma=\sqrt{15\times0.9\times(1 - 0.9)}=\sqrt{1.35}\approx1.16\).

A binomial distribution \(B(n,p)\) is skewed left when \(p>0.5\) (since the tail is on the side of the lower - probability values). Here, \(p = 0.9>0.5\).

Answer:

skewed left