Luanne made a photocopy of a drawing of a rectangle. The original drawing was 4.5 inches wide and 6 inches long. The copy was 6.
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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 find the inverse of a function, we make the independent variable the subject of the formula.
Thus, the inverse of the given function is evaluated as follows.
From the work show, it can be seen that Talib's work is correct.
Thus, the inverse of the given function is evaluated as follows.
From the work show, it can be seen that Talib's work is correct.