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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.

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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Please refer to the given lesson and sketch the normal curve
Example 3. 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? Solution: a. Step 1. Convert the score 50 to z-score Z= X-X S 50-45 = z = 1.25 Step 2. Sketch the normal curve. Let A = area above z = 1.25 A₁ = area between z = 0 and z = 1.25 A 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 x-X Z= = 38-45 4 z = -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 A₂ A₁ 01.25 45 50 A₁ 0 45
Transcribed Image Text:Example 3. 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? Solution: a. Step 1. Convert the score 50 to z-score Z= X-X S 50-45 = z = 1.25 Step 2. Sketch the normal curve. Let A = area above z = 1.25 A₁ = area between z = 0 and z = 1.25 A 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 x-X Z= = 38-45 4 z = -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 A₂ A₁ 01.25 45 50 A₁ 0 45
Evaluation: Solve the following problems. 1. In a Scien listributed, randoITTIS greater then rez and o5? 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 Scien listributed, randoITTIS greater then rez and o5? 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.
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