a large number of voltages show a mean of 118.5v and a population standard deviation of 1.20v. determine the percentage of data that falls between 116 and 120 volts.

Step-by-step explanation:

Hello!

X: voltage, it has a mean of μ = 118.5V and a standard deviation of σ = 1.20V.

Assuming the variable has a normal distribution, I'll use the standard normal distribution to calculate the probability that the voltage is between 116 and 120 volts.

P (116≤X≤120) = P (X≤120) - P (X≤116)

Using Z = (X - μ) / σ you now standardize the voltage values and get the cumulative probabilities from the tables of Z.

P (Z≤ (120-118.5) / 1.20) - P (Z≤ (116-118.5) / 1.20)

P (Z≤1.25) - P (Z≤-2.08) = 0.89435 - 0.01876 = 0.87559

87.559% of the data will be between 116 and 120 volts.

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