Given a normal distribution with mean 100 and standard deviation 10 , find the number of standard deviations the measurement is from the mean. Express the answer as a positive number. 112.8 112.8 is standard deviations away from the mean. (Type an integer or decimal.)

Step 1 ：Given a normal distribution with mean 100 and standard deviation 10, we are asked to find the number of standard deviations the measurement 112.8 is from the mean. This is also known as the z-score in statistics.

Step 2 ：The z-score is calculated by subtracting the mean from the measurement and then dividing by the standard deviation. In mathematical terms, this can be expressed as \( z = \frac{x - \mu}{\sigma} \), where \(x\) is the measurement, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step 3 ：Substituting the given values into the formula, we get \( z = \frac{112.8 - 100}{10} \).

Step 4 ：Solving the above expression, we find that the z-score is approximately 1.28.

Step 5 ：Thus, the measurement 112.8 is 1.28 standard deviations away from the mean.

Step 6 ：Final Answer: \(\boxed{1.28}\)