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theman300045
03.12.2021 •
Mathematics
Would you rather have 1520 of a pizza or 34 of a pizza? Explain your answer and how you solved the problem.
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Ответ:
I would rather have 34 of a pizza because the slice would be bigger
Step-by-step explanation:
Hope this helps
Ответ:
0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.
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
and standard deviation
, the z-score of a measure X is given by:
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 p-value, 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
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean 790 and standard deviation 92.
This means that![\mu = 790, \sigma = 92](/tpl/images/1267/7713/57568.png)
Samples of 98
This means that![n = 98, s = \frac{92}{\sqrt{98}}](/tpl/images/1267/7713/4076e.png)
What is the probability that the mean number of eggs laid would differ from 790 by less than 30?
This is the pvalue of Z when X = 790 + 30 = 820 subtracted by the pvalue of Z when X = 790 - 30 = 760. So
X = 820
By the Central Limit Theorem
X = 760
0.9994 - 0.0006 = 0.9988
0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.