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Question: A set of data has a normal distribution with a mean of 53 and a...

Question: A set of data has a normal distribution with a mean of 53 and a standard deviation of 6. Find the...

A set of data has a normal distribution with a mean of 53 and a standard deviation of 6. Find the percent of data within each interval...

a. from 47 to 65

b. from 41 to 47

c. greater than 59

d. less than 65

Please show all steps.

Note: a - d are NOT potential answers, they are subquestions. I would like to know the percent of data within each interval in a, b, c, and d.

Please show all the work, including any calculator steps taken. Please do not say "use calculator" - specify what exactly to do with it if you do use it.

Solutions

Expert Solution

Given, mean of normal distribution is : m = 53 and standard deviation is : = 6.

Then, probability density function f(x) is :

i.e.,

a) Now, P(47<x<65) =

Taking we get,

= 0.8186

b) Now, P(47<x<65) =

Taking we get,

= 0.1359

c) Now, P(x>59) =

Taking we get,

= 1

d) Now, P(x<65) =

Taking we get,

= 0.9772

milcah answered 2 years ago
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