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

The arithmetic mean, Arithmetic mean Arithmetic means is commonly know...

Arithmetic mean Arithmetic means is commonly known as average or mean it is acquired by first of all summing up the values provided and by dividing the total value by the tota

Differential equations, There isn't actually a whole lot to this section th...

There isn't actually a whole lot to this section this is mainly here thus we can get several basic concepts and definitions out of the way.  Most of the concepts and definitions in

Geometry problems, if a circles diameter is 42 mm its radius is ___________...

if a circles diameter is 42 mm its radius is _________________ because ________________________.

Logarithmic functions, If x = b y where both b > 0, x > 0, then we d...

If x = b y where both b > 0, x > 0, then we define y = log b x, which is read as "y is the log to the base b of x". This means that, log b x or y is the number to

Decimals, how will the decimal point move when 245.398 is multiplied by 10

how will the decimal point move when 245.398 is multiplied by 10

Consumer behavior, explain big 5 ppersonality model, suggest thier target m...

explain big 5 ppersonality model, suggest thier target market and one marketing strategiy for each .

saxon math, what is the muttiplied number of mutttiplacation calle

what is the muttiplied number of mutttiplacation called

Range, identify the range of h(x)=2x+1

identify the range of h(x)=2x+1

Find var (3x+8) where x is a random variable, If Var(x) = 4, find Var (3x+8...

If Var(x) = 4, find Var (3x+8), where X is a random variable. Var (ax+b) = a 2 Var x Var (3x+8) = 3 2 Var x = 36

Good investment, Realtors estimate that 23% of homes purchased in 2004 were...

Realtors estimate that 23% of homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most

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