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Contact [7]
2 years ago
14

A ski lift is designed with a total load limit of 20,000 pounds. It claims a capacity of 100 persons. An expert in ski lifts thi

nks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload
Mathematics
1 answer:
Yanka [14]2 years ago
5 0

Answer:

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n values of a distribution, the mean is \mu \times n and the standard deviation is \sigma\sqrt{n}

An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.

This means that \mu = 200*100 = 20000, \sigma = 30\sqrt{100} = 300

If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload

Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So

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

Z = \frac{20000 - 20000}{300}

Z = 0

Z = 0 has a pvalue of 0.5

1 - 0.5 = 0.5

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

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2 years ago
Vince weighs 160 pounds, and his friend Nadir weighs 140 pounds. Nadir calculated that his weight on another planet would be abo
vlabodo [156]
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cross multiply
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5 0
3 years ago
Read 2 more answers
the numbers of girls in the choir is 4 times the number of boys in the choir .the total number of students is 60..how many girls
Inessa05 [86]
First, make up some variables to represent the number of Girls and Boys in the choir.  

B = number of boys
G = number of girls

You know that there are 4 times as many girls in the choir as boys.  Therefore, the equation you can write is:
\frac{B}{G} =  \frac{1}{4}

If you cross-multiply, then you get the simplified equation:
G = 4B

Intuitively this makes sense since if you multiplied the number of boys in the class by 4, that would be equal to the number of girls you have.

Now, we know that the total class size is 60. So girls plus boys equals 60:
G+B = 60

To solve the equation, replace the G in this equation with the replacement you found before, 4B.
G + B = 60 -->
4B + B = 60 -->
5B = 60 -->
B = 12

However, you are trying to find the number of girls, so plug the answer back into your equation.
G + B = 60 -->
G + 12 = 60 -->
G + 12 -12 = 60 - 12 -->
G = 48

The number of girls you have is 48.

6 0
3 years ago
NEED HELP URGENT!! How do I solve this on number 30?(please go through the steps)
tatiyna

x^2+6x-5=0

x^2=2x

2x+6x-5=0

2x+6x=8x

8x-5=0

+5 +5

(if you don’t know what I’m doing here is that I’m removing the negative 5 by putting a positive 5 since both of them make 0. Also the “x” always stay alone and the unit stays as the unit)

(I putted the positive under the 0 because what u do to the unit you need to do the same thing with the other.)

8x/8=5/8

(If ur lost here it means dividing.)

The answer

X=0.625

(btw I’m not really sure if this is right so um don’t really trust me in this lol)

3 0
3 years ago
Which equation has a graph that is a parabola with a vertex at (–2, 0)?
MaRussiya [10]

Answer:

The vertex of a quadratic equation corresponds to the point where the maximum or minimum value is located.

If the function has a positive leading coefficient, the vertex corresponds to the minimum value.

If it has a negative leading coefficient,  the vertex corresponds to the maximum valuevalue

If the vertex is located at

(–2, 0)

The possibilities are

y =  (x-2)^2

or,

y = - (x-2)^2

Since the problem tells us the answer, we adopt the positive values

Answer:

y =  (x-2)^2

See attached picture

6 0
2 years ago
Read 2 more answers
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