8 is 20% of what number?

An airplane has 100 seats for passengers. Assume that the probability that a person holding a ticket appears for the flight is 0

zmey [24]

Answer:

96.33% probability that everyone who appears for the flight will get a seat

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

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

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 105, p = 0.9$

So

$\mu = E(X) = np = 105*0.9 = 94.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{105*0.9*0.1} = 3.07$

What is the probability that everyone who appears for the flight will get a seat

100 or less people appearing to the flight, which is the pvalue of Z when X = 100. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{100 - 94.5}{3.07}$

$Z = 1.79$

$Z = 1.79$ has a pvalue of 0.9633

96.33% probability that everyone who appears for the flight will get a seat

7 0

3 years ago

express the sum of each pair of numbers as a product of the greatest common factor and another sum 42 + 105

DochEvi [55]

42/6 = 7 105/15 = 7
Biggest common factor is 7.
not sure if that was the question

8 0

3 years ago

Read 2 more answers

72 inches=___ yards please and thank you for your help

I am Lyosha [343]

We know that:

$1yd=36in\text{.}$

Then:

$1in=\frac{1}{36}yd\text{.}$

Therefore:

$72in=72\cdot(\frac{1}{36}yd)\text{.}$

Simplifying the above result we get:

$72\cdot\frac{1}{36}yd=2yd\text{.}$

Answer:

$72\text{inches}=2\text{yards.}$

6 0

1 year ago

Jim and Mark start at the same place jim walks 15ft West and Mark Walks 12 feet North how far apart are the boys when they finis

r-ruslan [8.4K]

The two points where they end and the point where they start form a right triangle, one leg is 12, the other leg is 15, you need to find the hypotenuse.
use the Pythagorean theorem: 12²+15²=c²
c≈19
they are about 19 feet apart.

3 0

3 years ago

Brian is selling cookies at a bake sale. He earns $2.75 for each bag of cookies he sells. Write an equation to represent this sc

sesenic [268]

Let C equal bags of cookies
Let M equal money earned

2.75c=m

Probably not enough sorry if it isn't

5 0

3 years ago

Read 2 more answers