Mathematics, 12.03.2021 15:30 cia196785920

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 thinks 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

Answers: 2

Show answers

Answers

Answer from: abbygriffin2009

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

Answer from: Quest

2 over 5 and 4 over 15

don’t know last one sorry

step-by-step explanation:

Answer from: Quest

should have been evaluated with one odd value and one even value. the expressions have equivalent values when . when , the first expression has a value of 3 and the second

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 17:50

Adriana sold 50 shares of a company’s stock through a broker. the price per share on that day was $22.98. the broker charged her a 0.75% commission. what was adriana’s real return after deducting the broker’s commission? a. $8.62 b. $229.80 c. $1,140.38 d. $1,149.00

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

What are different types of statistical programs

Answers: 2

Answer

Mathematics, 21.06.2019 18:40

Which of the following would be a good name for the function that takes the weight of a box and returns the energy needed to lift it?

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Given ab and cb are tangents of p, and m =10°. what is the measure of abp?