Mathematics, 05.05.2020 17:01, raven681

The capacity of n elevator is 12 people or 1968 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 1968/12=164 pounds. Suppose the people have weights that are normally distributed with a mean of 171 lb and a standard deviation of 34 lb.

a. find the probability that if a person is randomly selected, his weight will be greater than 164 pounds.

The probability is approximately ___

b. Find the probability that 12 randomly selected people will have a neam that is greater than 164 pounds.

Answers: 2

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answered: GodlyGamer8239

a) 58.32% probability that his weight will be greater than 164 pounds.

b) 76.11% probability that 12 randomly selected people will have a neam that is greater than 164 pounds.

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 normally distributed samples are 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.

In this problem, we have that:

$\mu = 171, \sigma = 34$

a. find the probability that if a person is randomly selected, his weight will be greater than 164 pounds.

This is 1 subtracted by the pvalue of Z when X = 164. So

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

$Z = \frac{164 - 171}{34}$

Z = -0.21

Z = -0.21 has a pvalue of 0.4168

1 - 0.4168 = 0.5832

58.32% probability that his weight will be greater than 164 pounds.

b. Find the probability that 12 randomly selected people will have a neam that is greater than 164 pounds.

Now $n = 12, s = \frac{34}{\sqrt{12}} = 9.81$

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

By the Central Limit Theorem

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

$Z = \frac{164 - 171}{9.81}$

Z = -0.71

Z = -0.71 has a pvalue of 0.2389

1 - 0.2389 = 0.7611

76.11% probability that 12 randomly selected people will have a neam that is greater than 164 pounds.

answered: Guest

the correct answer is a) they believe they have a "just cause."

islamic terrorists justify their violent actions because they believe they have a "just cause."

every act of terrorism of islamic sects is done “in the name of allah”. that justifies their actions. islam people who commit those terrorist attacks are not afraid to die. that is why the attacks have horrible consequences. they know they are going to die and they are proud to do it because it is in the name of allah, so it is justified and is for a “good cause.”

since the very beginning of the conflict with israel, islam is fighting a “sacred war”, respecting the words stated in the qur’an. they fight against the domination of the western countries and to defend their occupied territories.

answered: Guest

if you're trying to figure out how much each ounce cost it would be 0.20

cents each ounce