Answered: Given a normal distribution with…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 7E

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Question

Given a normal distribution with muμequals=35 and sigmaσequals=66, find (a) the normal curve area to the right of xequals=18; (b) the normal curve area to the left of xequals=27;(c) the normal curve area between xequals=37 and xequals=48; (d) the value of x that has 70% of the normal curve area to the left; and (e) the two values of x that contain the middle 75% of the normal curve area.

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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