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jaymoney0531
20.03.2020 •
Mathematics
Shelia's measured glucose level one hour after a sugary drink varies according to the normal distribution with μ = 116 μ=116 mg/dl and σ = 11.3 σ=11.3 mg/dl. What is the level L L such that there is probability only 0.01 that the mean glucose level of 2 test results falls above L L ? Give your answer precise to one decimal place.
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Ответ:
The level is L = 134.6
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 sample means with size n can be approximated to a normal distribution with mean
and standard deviation ![s = \frac{\sigma}{\sqrt{n}}](/tpl/images/0556/6530/a95e6.png)
In this problem, we have that:
What is the level L L such that there is probability only 0.01 that the mean glucose level of 2 test results falls above L?
This is X when Z has a pvalue of 1-0.01 = 0.99. So it is X when Z = 2.325.
By the Central limit theorem
The level is L = 134.6
Ответ:
The baton will not fit in the rectangular box
Step-by-step explanation:
step 1
Find the diagonal of the base of the rectangular base and then compare with the length of the baton
Applying the Pythagoras Theorem
Let
x ----> the length of the diagonal base of rectangular box
we know that
therefore
The baton will not fit in the rectangular box