The time for a professor to grade a student’s homework in statistics is normally distributed with a mean of 14.2 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 18 minutes to grade?Multiple Choice0.64920.83160.19830.9713
Question
The time for a professor to grade a student’s homework in statistics is normally distributed with a mean of 14.2 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 18 minutes to grade?Multiple Choice0.64920.83160.19830.9713
Solution
To solve this problem, we need to use the concept of Z-score in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.
Step 1: Identify the mean, standard deviation, and the value for which we need to find the probability. Here, mean (μ) = 14.2 minutes, standard deviation (σ) = 2.0 minutes, and the value (X) = 18 minutes.
Step 2: Calculate the Z-score using the formula Z = (X - μ) / σ. Substituting the given values, we get Z = (18 - 14.2) / 2 = 1.9.
Step 3: Look up this Z-score in the Z-table (also known as the standard normal distribution table) to find the probability. The value for 1.9 in the Z-table is 0.9713.
So, the probability that randomly selected homework will require less than 18 minutes to grade is 0.9713.
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