Answered: Terri Vogel, an amateur motorcycle…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter9: Solving Quadratic Functions

Section: Chapter Questions

Problem 4CA

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Question

Terri Vogel, an amateur motorcycle racer, averages 129.5 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.27 seconds . The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the proportion of her laps that are completed between 128.36 and 130.41 seconds.

c. The fastest 4% of laps are under seconds.

d. The middle 40% of her laps are from seconds to seconds

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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