Mathematics, 15.11.2019 17:31, amandaestevez030

Amanufacturer knows that their items have a normally distributed lifespan, with a mean of 13.2 years, and standard deviation of 3.1 years. if you randomly purchase 12 items, what is the probability that their mean life will be longer than 12 years?

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answered: NBASTARK4523

There is a 91.15% probability that their mean life will be longer than 12 years.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

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.

In this problem, we have that:

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.2 years, and standard deviation of 3.1 years. This means that $\mu = 13.2, \sigma = 3.1$ .

If you randomly purchase 12 items, what is the probability that their mean life will be longer than 12 years?

There are 12 items, so n = 12 .

This is 1 subtracted by the pvalue of Z when X = 12 .

By the Central Limit Theorem, we use the standard deviation of the sample in the Z score formula. That is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{3.1}{\sqrt{12}} = 0.89$

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

$Z = \frac{12-13.2}{0.89}$

Z = -1.35

Z = -1.35 has a pvalue of 0.0885

This means that there is a 1-0.0885 = 0.9115 = 91.15% probability that their mean life will be longer than 12 years.

answered: Guest

answer: yes, he is correct

step-by-step explanation: 10x-1=59

1-1=0 59+1=60

60/10=x=6

answered: Guest

step-by-step explanation:

in the absence of parentheses, i will have to make some assumptions: i interpret your (3x+5/y^6)(4y^3/5) to mean:

3x + 5 4y^(3/5) (3x + 5)(4)

* =

y^6 1 y^(6-3/5)

if this is not what you expected, repost your question using parentheses to indicate whether you meant

4y^3

or 4y^(3/5)

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Amanufacturer knows that their items have a normally distributed lifespan, with a mean of 13.2 years...