airrish
16.03.2020 •
Mathematics
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.1 years, and standard deviation of 1.3 years. If you randomly purchase one item, what is the probability it will last longer than 7 years
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Ответ:
24.51% probability it will last longer than 7 years
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
If you randomly purchase one item, what is the probability it will last longer than 7 years
This is 1 subtracted by the pvalue of Z when X = 7. So
has a pvalue of 0.7549
1 - 0.7549 = 0.2451
24.51% probability it will last longer than 7 years
Ответ:
c
Step-by-step explanation: