Answer:
The probability that there will be enough seats for all people who turn up is 0.78
Step-by-step explanation:
Given:
A = 500
B = 550
Since it is known from experience that 10% of people who bought tickets don't show up, to find the probability that there will be enough seats for those who show up, we have:
Percentage that will turn up = 100℅ - 10℅ = 90℅
Since 90℅ will turn up, that means the number of passengers will be less than 500.
Therefore for P less than or equal to 500, we use:
P ( X <_ 500) =
= [500 + 0.5 - (550 * 0.9)] / sqrt*(550 * 0. 9 * 0.1)
= 0.78
Therefore, the probability that there will be enough seats for all people who turn up is 0.78
Answer:
Therefore, the probability is P=0.76.
Step-by-step explanation:
We kmow that a plane has 500 seats. From experience, it's known that 10% of people who have bought the ticket do not show up.
We know that a 550 tickets have been sold for one flight.
We get that q=10%=0.1, and p=1-q=1-0.1=0.9.
We use the central limit Theorem and we use the table, we calculate the probability:
[tex]P(X\leq 500)=\Phi(z)=\Phi\left(\frac{500-550\cdot 0.9}{\sqrt{550\cdot 0.9\cdot 0.1}}\right)=\Phi\left(\frac{5}{7.0356}\right)=\Phi(0.7106)=0.76\\[/tex]
Therefore, the probability is P=0.76.
