Answered: 4. The time taken to boil a kettle is…

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

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

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1
of 2
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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

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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