Mathematics, 08.03.2021 20:40 keigleyhannah30

Your flight has been delayed: At Denver International Airport, 85% of recent flights have arrived on time. A sample of flights is studied. Round the probabilities to four decimal places. Part 1 of 4 (a) Find the probability that all of the flights were on time. The probability that all of the flights were on time is . Part 2 of 4 (b) Find the probability that exactly of the flights were on time. The probability that exactly of the flights were on time is . Part 3 of 4 (c) Find the probability that or more of the flights were on time. The probability that or more of the flights were on time is . Part 4 of 4 (d) Would it be unusual for or more of the flights to be on time

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Answer from: g0606997

a) $P(X = n) = (0.85)^{n}$

b) $P(X = x) = C_{n,x}.(0.85)^{x}.(0.15)^{n-x}$

$P(X \geq x) = P(X = x) + P(X = x+1) + ... + P(X = n)$

For each value, we use

$P(X = x) = C_{n,x}.(0.85)^{x}.(0.15)^{n-x}$

d) If $x E(X) + \sqrt{V(X)}$ , yes, otherwise no

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrived on time, or it did not. Flights are independent. This means that we use the binomial probability distribution to solve this question.

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.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

A measure is said to unusual if it is more than 2.5 standard deviations from the mean.

85% of recent flights have arrived on time.

This means that p = 0.85

(a) Find the probability that all of the flights were on time.

This is P(X = n) , in which n is the size of the sample studied.

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

$P(X = n) = C_{n,n}.(0.85)^{n}.(0.15)^{n-n}$

$P(X = n) = (0.85)^{n}$

(b) Find the probability that exactly x of the flights were on time.

Exactly x of the flights: So

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

$P(X = x) = C_{n,x}.(0.85)^{x}.(0.15)^{n-x}$

This is

$P(X \geq x) = P(X = x) + P(X = x+1) + ... + P(X = n)$

For each value, we use

$P(X = x) = C_{n,x}.(0.85)^{x}.(0.15)^{n-x}$

(d) Would it be unusual for x or more of the flights to be on time?

If $x E(X) + \sqrt{V(X)}$ , yes, otherwise no

Answer from: Quest

answer: just subtact the units and then add the non negative : happy to

step-by-step explanation:

Answer from: Quest

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

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