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Suppose human weights are normally distributed with mean 175 and standard deviation 36 pounds. A helicopter is evacuating people from a building surrounded by zombies, and this helicopter can fit 9 people and with a maximum weight of 1800 pounds, i.e., an average of 200 pounds per person. If 9 people are randomly chosen to be loaded on this helicopter, what is the probability that it can safely lift off (i.e., the average weight of a person in the helicopter is less than 200)?

Answers

Answer 1

Answer:

Answer:

$P(\bar X <200)=P(Z<(200-175)/((36)/(√(9)))=2.083)$

And using a calculator, excel or the normal standard table we have that:

$P(Z<2.083)=0.981$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(175,36)$

Where $\mu=175$ and $\sigma=36$

They select a sample size of n=9 people.The distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, (\sigma)/(√(n)))$

And we want to find this probability:

$P(\bar X <200)$

In order to the helicopter can safely lift off. We can use the z score formula given by:

$z = (\bar X -\mu)/((\sigma)/(√(n)))$

$P(\bar X <200)=P(Z<(200-175)/((36)/(√(9)))=2.083)$

And using a calculator, excel or the normal standard table we have that:

$P(Z<2.083)=0.981$

Related Questions

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.2 years and a standard deviation of 0.6 years. He then randomly selects records on 38 laptops sold in the past and finds that the mean replacement time is 3.9 years. Assuming that the laptop replacement times have a mean of 4.2 years and a standard deviation of 0.6 years, find the probability that 38 randomly selected laptops will have a mean replacement time of 3.9 years or less.
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Write the addition equation as a multiplication equation.8 + 8 +8= 24
The ratio of green marbles to total marbles in a bag is 2:9. The ratio of red marbles to total marbles in the same bag is 1:3. Which of the following statements is true
I'LL MARK THE BRAINLIESTWhat is the exact circumference of the circle?

Please help me with my math!!!!!!!!!

Answers

12.8 km per hour

51.2 km in 4 hours

What is a root function of the polynomial function F(x)= x^3 + 3x^2 - 5x - 4

Answers

This is your answer
Xxxx

Step-by-step explanation:

Factor by grouping.

f(x) = x³ + 3x² − 5x − 4

f(x) = x³ + 3x² − 4x − x − 4

f(x) = x (x² + 3x − 4) − (x + 4)

f(x) = x (x − 1) (x + 4) − (x + 4)

f(x) = (x² − x) (x + 4) − (x + 4)

f(x) = (x² − x − 1) (x + 4)

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Which of the following best describes the form of the sampling distribution of the sample mean for this situation? a. Approximately normal because the sample size is small relative to the population size b. Approximately normal because of the central limit theorem c. Exactly normal d. None of these alternatives is correct.

Answers

None of the given alternatives described the Sample mean for the situation. A complete solution is below.

Given values are:

Sample size,

n = 17

Mean,

μ = 36

Standard deviation,

σ = 8

As we know,

The Standard deviation of sample mean,

→ $(\sigma)/(√(n) )$

By substituting the values, we get

→ $(8)/(√(17) )$

→ $(8)/(4.13)$

→ $1.94$

Thus the response i.e., "option d" is appropriate.

Learn more:

brainly.com/question/16555520

Answer:

Step-by-step explanation:

Find the general solution of the following equation: y'(t) = 3y -5

Answers

Answer:

The general solution of the equation is y = $(A)/(3)e^(3t)$ + 5

Step-by-step explanation:

Since the differential equation is given as y'(t) = 3y -5

The differential equation is re-written as

dy/dt = 3y - 5

separating the variables, we have

dy/(3y - 5) = dt

integrating both sides, we have

∫dy/(3y - 5) = ∫dt

∫3dy/[3(3y - 5)] = ∫dt

(1/3)∫3dy/(3y - 5) = ∫dt

(1/3)㏑(3y - 5) = t + C

㏑(3y - 5) = 3t + 3C

taking exponents of both sides, we have

exp[㏑(3y - 5)] = exp(3t + 3C)

3y - 5 = $e^(3t)e^(3C)$

3y - 5 = $Ae^(3t)$ $A = e^(3C)$

3y = $Ae^(3t)$ + 5

dividing through by 3, we have

y = $(A)/(3)e^(3t)$ + 5

So, the general solution of the equation is y = $(A)/(3)e^(3t)$ + 5

Give two examples of addition of two mixed numbers with different denominators
SHOW ALL STEPS

Answers

Answer:

First Example: 3 1/2 + 4 3/4, Second Example: 6 3/8 + 7 9/15

Extra Example: 8 4/20 + 3 5/10

Step-by-step explanation:

First Example:

1/2 + 3/4

1/2 is equal to 2/4 so it is now compatible to be added to 3/4.

2/4 + 3/4

= 5/4

Now for the mixed numbers since its 3 and 4, 3 + 4 = 7.

Final answer is 7 5/4.

Second Example:

3/8 + 9/15

9/15 can be reduced to 3/5

Now the equation is 3/8 + 3/5

= 15/40 + 24/40 is an equivalent equation

15/40 + 24/40

= 39/40

Now for the mixed numbers since its 6 and 7, 6 + 7 = 13

Final answer is 13 39/40.

I am going to include one last example just in case you need one:

Third Example:

4/20 + 5/10

We can reduce these to

1/5 + 1/2

= 2/10 + 5/10 is the equivalent equation

2/10 + 5/10

= 7/10

Now for the mixed numbers since its 8 and 3, 8 + 3 = 11.

Final answer is 11 7/10.

I Hope this helps!

Which expression represents "6 more than x"?
x - 6
6x
x + 6
6 - x

Answers

x+6
this is because + means more, so 6 more

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