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Hannahrose911
16.03.2020 •
Mathematics
The body temperatures of adults are normally distributed with a mean of 98.6degrees° F and a standard deviation of 0.60degrees° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4degrees° F.
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Ответ:
97.72% probability that their mean body temperature is greater than 98.4degrees° F.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples can be 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
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation ![s = \frac{\sigma}{\sqrt{n}}](/tpl/images/0549/2229/a95e6.png)
In this problem, we have that:
If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4degrees° F.
This is 1 subtracted by the pvalue of Z when X = 98.4. So
By the Central Limit Theorem
1 - 0.0228 = 0.9772
97.72% probability that their mean body temperature is greater than 98.4degrees° F.
Ответ:
multiple allele inheritance is traits controlled by more than 2 alleles (ex: pigeons having 3 alleles of one gene govern their feather color).