According to Forbes magazine, the 2023 average starting salary for new college graduates in humanities was $50,681 The average starting salary for new college graduates in engineering was $73,922 (Forbes.com website). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in humanities is $14,000 . Assume that the standard deviation for starting salaries for new college graduates in engineering is $19,000 . a. What is the probability that a new college graduate in engineering will earn a starting salary of at least $80,000 (to 4 decimals)? b. What is the probability that a new college graduate in humanities will earn a starting salary of at least 80,000 (to 4 decimals)? c. What is the probability that a new college graduate in humanities will earn a starting salary less than 50,000 (to 4 decimals)? d. How much would a new college graduate in engineering have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in humanities (to 0 decimal)? $ What percentage of engineering students are expected to earn a starting salary higher than 99% of all starting salaries of humanities graduates (to 2 decimals)?

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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According to Forbes magazine, the 2023 average starting salary for new college graduates in humanities was $50,681 The average starting salary for new college graduates in engineering was $73,922 (Forbes.com website). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in humanities is $14,000 . Assume that the standard deviation for starting salaries for new college graduates in engineering is $19,000 .

a. What is the probability that a new college graduate in engineering will earn a starting salary of at least $80,000 (to 4 decimals)?

b. What is the probability that a new college graduate in humanities will earn a starting salary of at least 80,000 (to 4 decimals)?

c. What is the probability that a new college graduate in humanities will earn a starting salary less than 50,000 (to 4 decimals)?

d. How much would a new college graduate in engineering have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in humanities (to 0 decimal)?

What percentage of engineering students are expected to earn a starting salary higher than 99% of all starting salaries of humanities graduates (to 2 decimals)?

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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