236 CHAPTER 5 Normal Probability Distributions Interpreting Graphs of Normal Distributions The scaled test scores for the New York State Grade 6 Mathematics Operational Test are normally distributed. The normal curve shown below represents this distribution for a recent year. What is the mean test score? Estimate the standard deviation of this normal distribution. (Adapted from New York State Education Department) x Scaled test score Mathematics Test 520 560 600 640 680 SOLUTION x Scaled test score 520 560 600 640 680 Because a normal curve is symmetric about the mean, you can estimate that ≈ 600. Because the inflection points are one standard deviation from the mean, you can estimate that ≈ 20. μ σ The scaled test scores for the New York State Grade 6 Mathematics Operational Test are normally distributed with a mean of about 600 and a standard deviation of about 20. Interpretation Using the Empirical Rule (see Section 2.4), you know that about 68% of the scores are between 580 and 620, about 95% of the scores are between 560 and 640, and about 99.7% of the scores are between 540 and 660. TRY IT YOURSELF 2 The reading subscores for the New York State Grade 6 English Language Arts Operational Test are normally distributed. The normal curve shown below represents this distribution for a recent year. What is the mean subscore? Estimate the standard deviation of this normal distribution. (Adapted from New York State Education Department) Subscore x Reading Test 0.6 6.4 12.2 18.0 23.8 29.6 35.4 Answer: Page A39 Tech Tip You can use technology to graph a normal curve. For instance, you can use a TI-84 Plus to graph the normal curve in Example 2. Plot1 Plot2 Plot3 Y3= Y4= Y5= Y6= Y2= Y7= Y1=normalpdf(X,600,20) 520 680 0.025 0 EXAMPLE 2
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