Sums of Independent Random Variables

In summary, the conversation is about finding the probability that the average IQ of 10 randomly selected students from a certain college is at least 112, given that the distribution of IQ for a single student from that college is N(110,16). The person asking the question initially calculates the probability to be 0.1056, but then realizes their mistake and correctly calculates it to be 0.0571.
  • #1
WHB3
21
0

Homework Statement



The distribution of the IQ of a randomly selected student from a certain college is N(110,16). What is the probability that the average of the IQ's of 10 randomly selected students from this college is at least 112?


Homework Equations



I think we need P(Sample Mean - 110 >= 2)


The Attempt at a Solution



My solution was Probability = (112-110)/1.6 = 1.25; 1-I(1.25)= 1-.8944 =.1056

The answer in the book is .0571, so I know I'm going wrong somewhere.

Any ideas?
 
Physics news on Phys.org
  • #2
No need to respond, guys. I have found the error of my ways. I forgot that the std Error equals the std deviation divided by the sqr. root of the sample size. Working with that would have brought me to the Probability = 1-I(1.58) = 1-1.9429 =.0571. Thanks, anyway!
 

What are "Sums of Independent Random Variables"?

"Sums of Independent Random Variables" refer to the mathematical concept of adding together multiple random variables that are independent of each other. This is commonly seen in probability and statistics when analyzing the outcomes of multiple events or experiments.

Why is it important to understand Sums of Independent Random Variables?

Understanding Sums of Independent Random Variables is important because it allows us to accurately predict the outcomes of multiple independent events or experiments. This is crucial in many fields such as finance, engineering, and biology.

How do you calculate the sum of independent random variables?

The sum of independent random variables is calculated by simply adding together the individual random variables. This follows the basic rules of addition, but it is important to note that the variables must be independent for this rule to apply.

What is the Central Limit Theorem and how does it relate to Sums of Independent Random Variables?

The Central Limit Theorem states that the sum of a large number of independent random variables will tend towards a normal distribution. This means that even if the individual random variables are not normally distributed, their sum will approach a normal distribution as the number of variables increases.

What are some real-world applications of Sums of Independent Random Variables?

Sums of Independent Random Variables have many applications in various fields. For example, in finance, the returns of multiple stocks can be added together to predict the overall return of a portfolio. In biology, the effects of multiple genetic factors can be summed to determine the likelihood of a certain trait being expressed. In engineering, the forces acting on a structure can be added together to determine the overall stress on the structure.

Similar threads

Three independent random variables having Normal distribution
    • Calculus and Beyond Homework Help
Replies
7
Views
1K
Finding Probability Density Functions for Independent Random Variables
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Testing of the hypothesis of variance
    • Calculus and Beyond Homework Help
Replies
8
Views
1K
What is the distribution of the sum of n iid Bernoulli random variables?
    • Calculus and Beyond Homework Help
Replies
1
Views
729
I Linear regression and random variables
    • Set Theory, Logic, Probability, Statistics
Replies
30
Views
2K
I Sample space, outcome, event, random variable, probability...
    • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
I Randomly Stopped Sums vs the sum of I.I.D. Random Variables
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
Choose a ball at random from a randomly selected box - alternative way
    • Precalculus Mathematics Homework Help
Replies
10
Views
960
Independence of Random Variables
    • Calculus and Beyond Homework Help
Replies
6
Views
1K
B Definition of a random variable in quantum mechanics?
    • Quantum Physics
Replies
12
Views
731

Hot Threads

Recent Insights

Back
Top