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
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ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
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Chapter11: Data Analysis And Displays
Section: Chapter Questions
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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
fall between?
T
W
Transcribed Image Text:Page 1 of 2 ZOOM 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 fall between? T W
Expert Solution
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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