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3. Use proportional reasoning to answer the following question.
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Answer:
82.31% of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter
Step-by-step explanation:
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.
In this problem, we have that:
Approximately what percentage of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter?
This is the pvalue of Z when X = 5.4 subtracted by the pvalue of Z when X = 4.2. So
X = 5.4
has a pvalue of 0.9842
X = 4.2
has a pvalue of 0.1611
0.9842 - 0.1611 = 0.8231
82.31% of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter