Respuesta :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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:
[tex]\mu = 0.8551, \sigma = 0.0518[/tex]
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
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.8544 - 0.8551}{0.0518}[/tex]
[tex]Z = -0.01[/tex]
[tex]Z = -0.01[/tex] has a pvalue of 0.4960
1 - 0.4960 = 0.5040
50.40% probability that it weighs more than 0.8544 g.
