Find probabilities for the standard normal distribution, Mathematics

Assignment Help:

Q. Find Probabilities for the Standard Normal Distribution?

Ans.

Suppose the history teacher decides to distribute the final grades of his class with a normal distribution. He wants to give a score of C or higher to all students who score within 1.1 standard deviations of the mean. What percentage of students will receive a mark of C or greater?

Solution:

463_standard deviations.gif


Use the table of probabilities for the normal standard distribution. The table shows that . This means that 86.43% of students have a z-score less than 1.1.

789_standard deviations1.gif


We know that 50% of the students scored below the mean. Thus, 86.43% or 50% = 36.43% of the students scored between the mean and 1.1 standard deviations above it.

Since the normal distribution is symmetric, there is also 36.43% of students which scored between a z-score of 1.3 and the mean.

The total percentage of students within 1.1 standard deviations of the mean is .

Thus 72.86% of the students in the history class will get a final mark of C or higher.


Related Discussions:- Find probabilities for the standard normal distribution

Algebra 1, Im having trouble with this word problem: The three Math Idol j...

Im having trouble with this word problem: The three Math Idol judges have been eliminating contestants all day! The number of one-step equations and two-step equations who have be

Shares and dividend, what all can be the table contents for my maths projec...

what all can be the table contents for my maths project on shares and dividend

Example of multiplication of matrix, Given So calculate AB. Sol...

Given So calculate AB. Solution The new matrix will contain size 2 x 4. The entry in row 1 and column 1 of the new matrix will be determined by multiplying row 1 of

Evaluate infinity limit into the polynomial , Example   Evaluate following...

Example   Evaluate following limits. Solution Here our first thought is probably to just "plug" infinity into the polynomial & "evaluate" every term to finds out the

Applications of rational numbers, Kaylee makes 56 packages in seven hours T...

Kaylee makes 56 packages in seven hours Taylor makes 20% more packages in nine hours who makes more packages per hour

Even and odd functions, Even and Odd Functions : This is the final topic ...

Even and Odd Functions : This is the final topic that we have to discuss in this chapter.  Firstly, an even function is any function which satisfies,

Aggregation and augmentation, Previously discussed how important it is to e...

Previously discussed how important it is to expose children to a variety of verbal problems involving the concept that they are trying to learn. Children attach meaning to the abst

What is common triangles, Q. What is Common Triangles? Ans. Some t...

Q. What is Common Triangles? Ans. Some triangles appear more commonly than others. You will come across two triangles repeatedly as you learn more about trigonometry. T

International marketing, what are challenges and solution of international ...

what are challenges and solution of international marketing

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd