Question

Suppose a plane has 500 seats. From experience, it's known that 10% of people who have bought the ticket do not show up. Now, 550 tickets have been sold for one flight. What is the probability that there will be enough seats for all people who turn up?

Answer 1

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 2

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:

$P(X\leq 500)=\Phi(z)=\Phi\left(\frac{500-550\cdot 0.9}{\sqrt{550\cdot 0.9\cdot 0.1}}\right)=\Phi\left(\frac{5}{7.0356}\right)=\Phi(0.7106)=0.76$

Therefore, the probability is P=0.76.