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1. In a Science test, the mean is 60 and the standard deviation is 6. Assuming the scores are normally distributed, what is the probability that a score picked at random is a. greater than 65? b. less than 70? c. between 50 and 65?

1. In a Science test, the mean is 60 and the standard deviation is 6. Assuming the scores are normally distributed, what is the probability that a score picked at random is a. greater than 65? b. less than 70? c. between 50 and 65?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Note: Please follow the steps in the given lesson and sketch the normal curve
Evaluation: Solve the following problems. 1. In a Science test, the mean is 60 and the standard deviation is 6. Assuming the scores are normally distributed, what is the probability that a score picked at random is a. greater than 65? b. less than 70? c. between 50 and 65? 2. A fifth grader takes a standardized achievement test (mean = 125, s = 15) and scores a 148. What is this child's percentile rank? 3. To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume that the test scores are normally distributed.
Transcribed Image Text:Evaluation: Solve the following problems. 1. In a Science test, the mean is 60 and the standard deviation is 6. Assuming the scores are normally distributed, what is the probability that a score picked at random is a. greater than 65? b. less than 70? c. between 50 and 65? 2. A fifth grader takes a standardized achievement test (mean = 125, s = 15) and scores a 148. What is this child's percentile rank? 3. To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume that the test scores are normally distributed.
Example 3. Solution: In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie a. above score 50? b. below score 38? a. Step 1. Convert the score 50 to z-score X-X Z = = 50-45 4 z = 1.25 Step 2. Sketch the normal curve. 0 45 Let A area above z = 1.25 A₁ = area between z = 0 and z = 1.25 A₂ = area of half the curve From the table, A₁ = 0.3944 A = A₂-A₁ = 0.5-0.3944 A = 0.1056 The probability that a score picked up at random will be above score 50 is 0.1056. b. Step 1. Convert the score 38 to z-score Z= X-X S 38-45 = 2= -1.75 Step 2. Sketch the normal curve. -1.75 38 Let A = area below z = -1.75 A₁ = area between z = 0 and z = -1.75 A₂ = area of half the curve From the table, A₁ = 0.4599 A = A₂-A₁ = 0.5-0.4599 A = 0.0401 The probability that a score picked up at random will lie below 38 is 0.0401. ← A₂ A1 A1 A2 A 1.25 50 0 45
Transcribed Image Text:Example 3. Solution: In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie a. above score 50? b. below score 38? a. Step 1. Convert the score 50 to z-score X-X Z = = 50-45 4 z = 1.25 Step 2. Sketch the normal curve. 0 45 Let A area above z = 1.25 A₁ = area between z = 0 and z = 1.25 A₂ = area of half the curve From the table, A₁ = 0.3944 A = A₂-A₁ = 0.5-0.3944 A = 0.1056 The probability that a score picked up at random will be above score 50 is 0.1056. b. Step 1. Convert the score 38 to z-score Z= X-X S 38-45 = 2= -1.75 Step 2. Sketch the normal curve. -1.75 38 Let A = area below z = -1.75 A₁ = area between z = 0 and z = -1.75 A₂ = area of half the curve From the table, A₁ = 0.4599 A = A₂-A₁ = 0.5-0.4599 A = 0.0401 The probability that a score picked up at random will lie below 38 is 0.0401. ← A₂ A1 A1 A2 A 1.25 50 0 45
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