From the past experience, a professor knows that the test score of a student taking his/herfinal exam is a random variable with mean 75 and variance 25. What can be said aboutthe probability that a student will score between 65 and 85.
Question
From the past experience, a professor knows that the test score of a student taking his/herfinal exam is a random variable with mean 75 and variance 25. What can be said aboutthe probability that a student will score between 65 and 85.
Solution
Given that the test score is a random variable with a mean (μ) of 75 and a variance (σ^2) of 25, we can infer that the standard deviation (σ) is the square root of the variance, which is 5.
The problem is asking for the probability that a student will score between 65 and 85. This is equivalent to asking for the probability that the student's score will be within ±1 standard deviation of the mean.
In a normal distribution, about 68% of values drawn from that distribution are within one standard deviation away from the mean. Therefore, we can say that there is approximately a 68% chance that a student will score between 65 and 85.
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