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Sagot :
Answer:
0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste
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 650 pounds and a standard deviation of 20 pounds.
This means that [tex]\mu = 650, \sigma = 20[/tex]
What is the probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste?
Less than 620:
pvalue of Z when X = 620. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{620 - 650}{20}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
More than 700:
1 subtracted by the pvalue of Z when X = 700. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 650}{20}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
Total:
0.0668 + 0.0062 = 0.073
0.073 = 7.3% probability that a randomly selected student produces either less than 620 or more than 700 pounds of solid waste
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