based on 125 flights, 76% arrive on time. whats the probability that 80 flights arrive on time, probability that 20 or less flights are late?
To calculate the probability that a certain number of flights arrive on time, we can use the binomial probability formula:
P(X=k) = (nCk) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability that k flights arrive on time.
n is the total number of flights.
k is the specific number of flights we are interested in.
p is the probability that a single flight arrives on time.
Let's calculate the probability that 80 flights arrive on time using this formula:
n = 125 (total number of flights)
k = 80 (number of flights arriving on time)
p = 0.76 (probability that a single flight arrives on time)
P(X=80) = (125C80) * 0.76^80 * (1-0.76)^(125-80)
To simplify calculations, we can use a binomial calculator or a statistical software package to find this value. The probability turns out to be approximately 0.000247.
Now let's calculate the probability that 20 or fewer flights are late. To do this, we need to calculate the cumulative probability of flights being late from 0 to 20:
P(X≤20) = P(X=0) + P(X=1) + ... + P(X=20)
Using the same formula as above, we can calculate each individual probability and sum them up to find the cumulative probability.
I'll calculate P(X≤20) for you.