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Solany6426
01.07.2021 •
Mathematics
The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 509 MPa with a standard deviation of 17 MPa. (a) What is the probability that a randomly chosen sample of glass will break at less than 509 MPa
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Ответ:
0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
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 509 MPa with a standard deviation of 17 MPa.
This means that![\mu = 509, \sigma = 17](/tpl/images/1387/7689/9aee9.png)
What is the probability that a randomly chosen sample of glass will break at less than 509 MPa?
This is the p-value of Z when X = 509. So
0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa
Ответ: