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, let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of...

let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of the number in setM is 14.what is the value of X?

How to subtract fractions involving negative numbers, Q. How to Subtract fr...

Q. How to Subtract fractions involving negative numbers? Ans. This is the same as adding them, but just remember the rule that two negatives on the same fraction cancel ou

Polar to cartesian conversion formulas, Polar to Cartesian Conversion Formu...

Polar to Cartesian Conversion Formulas x = r cos Θ y = r sin Θ Converting from Cartesian is more or less easy.  Let's first notice the subsequent. x 2 + y 2   = (r co

Second order differential equations, In the earlier section we looked at fi...

In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous secti

Power rule, Power rule: d(x n )/dx = nx n-1 There are really three ...

Power rule: d(x n )/dx = nx n-1 There are really three proofs which we can provide here and we are going to suffer all three here therefore you can notice all of them. T

What is polygon, What is polygon? A polygon is a shape with three or mo...

What is polygon? A polygon is a shape with three or more sides, in which each side touches another only at its endpoints. Some polygons that you are probably already familiar w

Luis runs rate of 11.7 feet per second how far does he run, Luis runs at a ...

Luis runs at a rate of 11.7 feet per second. How far does he run in 5 seconds? You must multiply 11.7 by 5; 11.7 × 5 = 58.5. To multiply decimals, multiply generally, then coun

Methods for doing integral, There are really three various methods for doin...

There are really three various methods for doing such integral. Method 1: This method uses a trig formula as,  ∫sin(x) cos(x) dx = ½ ∫sin(2x) dx = -(1/4) cos(2x) + c

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