Mathematics, 12.03.2020 06:14 jrassicworld4ever

At a certain airport, 75% of the flights arrive on time. A sample of 10 flights is studied. Assume each flight is independent of the others. Find the probability that eight or more of the flights will arrive on time.

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Answer from: chasadyyy

The probability that eight or more of the flights will arrive on time is 0.5256

Probabilities

Probabilities are used to determine the chances of events

The given parameters are:

Sample size: n = 10

The proportion of flights that arrive on time p = 0.75

The required probability is then represented as:

$P(x \ge 8)$

Binomial probability

This is calculated using the following binomial probability formula

$P(X = x) = ^nC_x p^x (1 - p)^{n -x}$

So, we have:

$P(x \ge 8) =P(x = 8) + P(x = 9) + P(x =10)$

This gives

$P(x \ge 8) = ^{10}C_8 \times 0.75^8 \times 0.25^2 +^{10}C_9 \times 0.75^9 \times 0.25 +^{10}C_{10} \times 0.75^{10} \times 0.25^0$

This gives

$P(x \ge 8) = 0.5256$

Hence, the probability is 0.5256

Read more about probabilities at:

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Answer from: Valrom

52.56% probability that eight or more of the flights will arrive on time.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it is on time, or it is not. The probability of a flight being on time is independent from other flights. So 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.

At a certain airport, 75% of the flights arrive on time.

This means that p = 0.75

A sample of 10 flights is studied.

This means that n = 10

Find the probability that eight or more of the flights will arrive on time.

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

In which

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

$P(X = 8) = C_{10,8}.(0.75)^{8}.(0.25)^{2} = 0.2816$

$P(X = 9) = C_{10,9}.(0.75)^{9}.(0.25)^{1} = 0.1877$

$P(X = 10) = C_{10,10}.(0.75)^{10}.(0.25)^{0} = 0.0563$

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.2816 + 0.1877 + 0.0563 = 0.5256$

52.56% probability that eight or more of the flights will arrive on time.

Answer from: Quest

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3 * 15/2 = 57 1/2

step-by-step explanation:

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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