IQ81 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 of the voltage is 0.5825V.

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:

False signal:

higher than 1.5V.

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 = 0.995. So when X = 1.5, Z = 2.575.

The standard deviation of the voltage is 0.5825V.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.