Write the correct function represented in the table below HELP ASAP
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Answer:
The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.
Step-by-step explanation:
To solve this problem, 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L ?
This is the value of X when Z has a pvalue of 1-0.01 = 0.99. So X when Z = 2.33.
By the Central Limit Theorem
The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.
to get the equation of any straight line, we simply need two points off of it, let's use those two points in the picture below.
keeping in mind that for the point-slope form, either point will do, in this case we used the second one, but the first one would have worked just the same.
