The middle 95% of a group of 1000 students got scores ranging from 50 to 90 on a math test. If the distribution of these scores is approximated by a normal distribution, about how many more if the students scored below a 60 on the test than scored above a 90?
The middle 95% of a group of 1000 students got scores
Normal Distribution: Understand the properties of the normal distribution, including the mean (μ) and standard deviation (σ), and how they affect the shape of the distribution.
Z-Scores: Know how to calculate Z-scores, which measure how many standard deviations a particular value is from the mean. The formula for a Z-score is (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
Percentiles: Understand how percentiles relate to the distribution of data. In this problem, you're looking at the middle 95%, which corresponds to the 2.5th percentile to the 97.5th percentile.
Probability: Familiarity with basic probability concepts is essential, such as how to find the probability of an event occurring within a range of values in a continuous distribution.
Standard Normal Distribution Table or Calculator: You may need access to a standard normal distribution table or calculator to find probabilities associated with specific Z-scores.
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