What is the signal change of 58 with the distributed mean of 35,standard deviation 10, using .o1 level
To calculate the signal change of 58 with the distributed mean of 35, standard deviation 10, using a 0.01 (0.1%) level, we need to use the concept of the z-score and the normal distribution.
Step 1: Calculate the z-score.
The z-score measures the number of standard deviations a data point is from the mean. It can be calculated using the formula: z = (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.
In this case, the data point (x) is 58, the mean (μ) is 35, and the standard deviation (σ) is 10. Plugging these values into the formula, we get:
z = (58 - 35) / 10
z = 2.3
Step 2: Determine the probability using a z-table.
The z-table is a table that provides the probability associated with different z-scores. We need to find the probability of getting a z-score of 2.3 or higher.
Since the z-table typically shows probabilities from the left-tail of the distribution, we will calculate the area to the left of 2.3 and subtract it from 1 to get the area to the right.
Using a z-table (either in print or online), the area to the left of 2.3 is approximately 0.9893. Subtracting this value from 1:
Area to the right = 1 - 0.9893
Area to the right = 0.0107
Step 3: Calculate the signal change.
The signal change represents the percentage of the distribution that falls within the calculated z-score. To get the signal change, we multiply the area to the right by 100:
Signal change = Area to the right * 100
Signal change = 0.0107 * 100
Signal change ≈ 1.07%
Therefore, the signal change of 58 with a distributed mean of 35, standard deviation 10, using a 0.01 (0.1%) level, is approximately 1.07%.