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

How many cubic centimetres of cork dust will be required?, A cylindrical ve...

A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between two vessels is fi

Cardioids and limacons - polar coordinates, Cardioids and Limacons Thes...

Cardioids and Limacons These can be split up into the following three cases. 1. Cardioids: r = a + a cos θ and r = a + a sin θ. These encompass a graph that is vaguel

Addition rule - probability rule, The Addition Rule: Mutually Exclusive Eve...

The Addition Rule: Mutually Exclusive Events P(A or B or C) = P(A) + P(B) + P(C) This can be represented by the Venn diagram as follows:

How many feet is the new length if the new area is 141, A rectangular garde...

A rectangular garden has a width of 20 feet and a length of 24 feet. If each side of the garden is increased through the similar amount, how many feet is the new length if the new

Find x if circle passes through -3, The centre of a circle is (2x - 1, 3x +...

The centre of a circle is (2x - 1, 3x + 1).Find x if the circle passes through (-3,-1) and the length of the diameter is 20 units.

Calculate the area and circumference of a circle, Calculate the area and ci...

Calculate the area and circumference of a circle: Calculate the area and circumference of a circle with a 3" radius.  Solution: A =      πr2

Equation of line which perpendicular to the given line, Perpendicular to th...

Perpendicular to the line given by 10 y + 3x= -2 For this part we desire the line to be perpendicular to 10 y + 3x= -2 & so we know we can determine the new slope as follows,

Determine the position and nature of stationary points, Question. Deter...

Question. Determine the position and nature of stationary points of the function? f(x,y)= y/x -x 2 +y 2

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