Answered: Central High School believes their…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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Question

Central High School believes their students have unusually high SAT scores on average. The school has 165 students.

Based on national data, the average SAT score is 1067 with a population standard deviation of 207. Assume SAT scores are normally distributed. Let X be the random variable representing the mean SAT scores for groups of 165 randomly selected students.

a. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X is approximately normal with a mean of and a standard error of the mean .

b. Find the z-score associated to a sample with a mean of 1109, using the sampling distribution. Round your answer to two decimal places.

c. Find the probability that a randomly selected sample of 165 students has a mean SAT score higher than 1109. Round your answer to 4 decimal places.

d. Central High School finds that for their students, the average SAT score is 1109. Are they justified in saying their students perform unusually well on the SAT?

a. No, because the probability that a sample of 165 students would score that much higher than the national average is more than 0.05, making it not unusual.

b. Yes, because the average score for Central High students is higher than the national average.

c. No, because it would be unlikely for a group of 165 students to score that high on average.

d. Yes, because the probability that a sample of 165 students would score that much higher than the national average is less than 0.05, making it unusual.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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