Answer:
50.40% probability that it weighs more than 0.8544 g.
Step-by-step explanation:
When the distribution is normal, we use 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 question, we have that:
![\mu = 0.8551, \sigma = 0.0518](https://tex.z-dn.net/?f=%5Cmu%20%3D%200.8551%2C%20%5Csigma%20%3D%200.0518)
If 1 candy is randomly selected, find the probability that it weighs more than 0.8544 g.
This is 1 subtracted by the pvalue of Z when X = 0.8544. So
![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{0.8544 - 0.8551}{0.0518}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B0.8544%20-%200.8551%7D%7B0.0518%7D)
![Z = -0.01](https://tex.z-dn.net/?f=Z%20%3D%20-0.01)
has a pvalue of 0.4960
1 - 0.4960 = 0.5040
50.40% probability that it weighs more than 0.8544 g.