What is the Normal Distribution Probability for the following numbers:where X is less than 107.46 for a mean of 116, and standard deviation of 26.68Level of difficulty = 1 of 3Please format to 2 decimal places.
Question
What is the Normal Distribution Probability for the following numbers:where X is less than 107.46 for a mean of 116, and standard deviation of 26.68Level of difficulty = 1 of 3Please format to 2 decimal places.
Solution
To find the normal distribution probability for X less than 107.46, we can use the standard normal distribution table or a calculator.
Step 1: Standardize the value of 107.46 using the formula: Z = (X - μ) / σ where X is the given value (107.46), μ is the mean (116), and σ is the standard deviation (26.68).
Z = (107.46 - 116) / 26.68 Z = -0.322
Step 2: Look up the standardized value (-0.322) in the standard normal distribution table or use a calculator to find the corresponding probability.
Using a standard normal distribution table, the probability corresponding to Z = -0.322 is 0.373.
Step 3: Format the probability to 2 decimal places. The normal distribution probability for X less than 107.46 is 0.37 (rounded to 2 decimal places).
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