Mathematics, 28.02.2020 04:29, mfreeman1096

Find the indicated probability. Round to three decimal places. An airline estimates that 91% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?

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answered: rizha55

0.66% probability that the number of people who show up will exceed the capacity of the plane

Step-by-step explanation:

For each person booked, there are only two possible outcomes. Either they show up, or they do not. The probability of a person not showing up is independent from other people. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

An airline estimates that 91% of people booked on their flights actually show up.

This means that p = 0.91

If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?

This is P(X 74) when n = 76 .

P(X 74) = P(X = 75) + P(X = 76)

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 75) = C_{76,75}.(0.91)^{75}.(0.09)^{1} = 0.0058$

$P(X = 76) = C_{76,76}.(0.91)^{76}.(0.09)^{0} = 0.0008$

P(X 74) = P(X = 75) + P(X = 76) = 0.0058 + 0.0008 = 0.0066

0.66% probability that the number of people who show up will exceed the capacity of the plane

answered: Guest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

answered: Guest

6e14 is the answer.

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Find the indicated probability. Round to three decimal places. An airline estimates that 91% of peop...