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Answer:
There is an 38.21% probability that we find this lifespan for our sample average, or something even shorter.
Step-by-step explanation:
Problems of normally distributed samples can be 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:
A manufacturing firm claims that the batteries used in laptop computers will last an average of 50 months. This means that .
We found that the sample had a average lifespan of 47.3 months, and a standard deviation of s = 9 months. What is the probability that we find this lifespan for our sample average, or something even shorter?
We have to find the pvalue of Z when .
We are working with a sample mean, so we use the standard deviation of the sample in the place of . That is
So
has a pvalue of 0.3821.
There is an 38.21% probability that we find this lifespan for our sample average, or something even shorter.