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Sagot :
Answer:
0.0051 = 0.51% probability that the thickness is less than 3.0 mm
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 4.8 millimeters (mm) and a standard deviation of 0.7 mm.
This means that [tex]\mu = 4.8, \sigma = 0.7[/tex]
(a) Probability that the the thickness is less than 3.0 mm
pvalue of Z when X = 3. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3 - 4.8}{0.7}[/tex]
[tex]Z = -2.57[/tex]
[tex]Z = -2.57[/tex] has a pvalue of 0.0051
0.0051 = 0.51% probability that the thickness is less than 3.0 mm
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