Answered: Given that X has a normal distribution…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 9PT

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Question

Given that X has a normal distribution with μ = 300 and σ = 50,
i) Find the probability that X assumes a value greater than 362.
ii) Find the probability that X assumes a value between 181.5 and 291.
iii) Find the probability that X assumes a value less than 362.
iv) Find the value of x such that it has 42.8% of the area to the left.

Note: Tabulated values are at the end

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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