4. The time taken to boil a kettle is normally distributed with a mean of 94 seconds and a standard deviation of 6. What times do the middle 30% of boils
4. The time taken to boil a kettle is normally distributed with a mean of 94 seconds and a standard deviation of 6. What times do the middle 30% of boils
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section: Chapter Questions
Problem 6CR
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Step 1
Define the Random Variable,
X : The time taken to boil a kettle
Given that,
X ~ N(94,62)
Therefore,
Z = (X - 94)/6 ~ N(0,1)
We know that Z (standard normal) is symmetric about 0.
First we will find the middle 30% of the Standard Normal distribution. Then we can find the bounds for X by , using
X = 94 + 6Z [ as Z = (X - 94)/6]
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