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Answer:
The mean is 9.65 ohms and the standard deviation is 0.2742 ohms.
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.
10% of all resistors having a resistance exceeding 10.634 ohms
This means that when X = 10.634, Z has a pvalue of 1-0.1 = 0.9. So when X = 10.634, Z = 1.28.
5% having a resistance smaller than 9.7565 ohms.
This means that when X = 9.7565, Z has a pvalue of 0.05. So when X = 9.7565, Z = -1.96.
We also have that:
So
The mean is
The mean is 9.65 ohms and the standard deviation is 0.2742 ohms.