Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). The scores follow a normal distribution. From published information the standard deviation is 6.4. On a particular campus, the mean score of those taking the MCAT is 25.0. a. A single student is chosen at random, what is the probability the individual’s score is less than 22? b. In a sample of 30 students, what is the sampling distribution of the average score, ?̅? c. What is the probability that the average score of 30 students is less than 22?

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). The scores follow a normal distribution. From published information the standard deviation is 6.4. On a particular campus, the mean score of those taking the MCAT is 25.0. a. A single student is chosen at random, what is the probability the individual’s score is less than 22? b. In a sample of 30 students, what is the sampling distribution of the average score, ?̅? c. What is the probability that the average score of 30 students is less than 22?

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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Question

a. A single student is chosen at random, what is the probability the individual’s score is less than 22?
b. In a sample of 30 students, what is the sampling distribution of the average score, ?̅?
c. What is the probability that the average score of 30 students is less than 22?

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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