Answer:
3.92% probability that, for an adult after a 12-hour fast, x is less than 53
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:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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:
![\mu = 90, \sigma = 21](https://tex.z-dn.net/?f=%5Cmu%20%3D%2090%2C%20%5Csigma%20%3D%2021)
What is the probability that, for an adult after a 12-hour fast, x is less than 53?
This is the pvalue of Z when X = 53.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{53 - 90}{21}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B53%20-%2090%7D%7B21%7D)
![Z = -1.76](https://tex.z-dn.net/?f=Z%20%3D%20-1.76)
has a pvalue of 0.0392
3.92% probability that, for an adult after a 12-hour fast, x is less than 53