Mathematics, 02.03.2020 21:00 BrandyLeach01

The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the probability that the mean of a sample of 36 people is greater than 10.

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Answer from: queenkick17

99.99% probability that the mean of a sample of 36 people is greater than 10.

Step-by-step explanation:

To solve this question, we have 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 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 $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 12, \sigma = 3.2, n = 36, s = \frac{3.2}{\sqrt{36}} = 0.533$

Find the probability that the mean of a sample of 36 people is greater than 10.

This probability is 1 subtracted by the pvalue of Z when X = 10. So

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

By the Central Limit Theorem

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

$Z = \frac{10-12}{0.533}$

Z = -3.75

Z = -3.75 has a pvalue of 0.0001

1 - 0.0001 = 0.9999

99.99% probability that the mean of a sample of 36 people is greater than 10.

Answer from: Quest

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!

Answer from: Quest

false

step-by-step explanation:

false. two legs of the trapezoid would be congruent, but the other two would not. were all the legs congruent, then we'd have a square; were the 2 shorter sides congruent and the 2 longer sides also congruent, we'd have a rectangle.

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