A signal in a communication channel is called a false signal if its voltage is higher than 1.5 volts in absolute value. (Note that the voltage can be positive or negative here.) Assume that the voltage of a signal is normally distributed with a mean of 0. What is the standard deviation of voltage such that the probability of a false signal is 0.005.

The standard deviation is 0.5338V.

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:

What is the standard deviation of voltage such that the probability of a false signal is 0.005.

This means that when X = 1.5, Z has a pvalue of 1-(0.005/2) = 0.9975. So when X = 1.5, Z = 2.81. Also when X = -1.5, Z has a pvalue of 0.0025. So Z = -2.81. Applying any of then, we find the standard deviation.

The standard deviation is 0.5338V.

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step-by-step explanation:

step-by-step explanation:

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