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kakasveta [241]
3 years ago
11

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, 55

0 tickets have been sold for one flight. What is the probability that there will be enough seats for all people who turn up?
Mathematics
2 answers:
oksano4ka [1.4K]3 years ago
7 0

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

Vikentia [17]3 years ago
6 0

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.

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