Respuesta :
Answer:
0.0062 = 0.62% probability of getting an amount between that is at least 7.5 oz.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 7 oz and a standard deviation of 0.2 oz.
This means that [tex]\mu = 7, \sigma = 0.2[/tex]
What is the probability of getting an amount between that is at least 7.5 oz?
This is 1 subtracted by the pvalue of Z when X = 7.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.5 - 7}{0.2}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability of getting an amount between that is at least 7.5 oz.
