bellam302
24.03.2020 •
Mathematics
Required information A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08 mm and standard deviation 0.01 mm. What is the probability that a randomly chosen book is more than 20.2 mm thick
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Ответ:
10.29% probability that a randomly chosen book is more than 20.2 mm thick
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 and standard deviation , the zscore 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 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 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.
For sums, we have that the mean is and the standard deviation is
In this problem, we have that:
Using the Cenral Limit Theorem
What is the probability that a randomly chosen book is more than 20.2 mm thick
This is 1 subtracted by the pvalue of Z when X = 20.2. So
By the Central Limit Theorem
has a pvalue of 0.8971
1 - 0.8971 = 0.1029
10.29% probability that a randomly chosen book is more than 20.2 mm thick
Ответ:
8.1
Step-by-step explanation:
delta math told me so