Solve Normal Distribution Homework with Mean 5, Standard Deviation 4

In summary, to solve this problem, you need to first understand that X is normally distributed with a mean of 5 and standard deviation of 4. You can use the normalCDF and inverse functions on the TI-84 calculator or the standard (x-mean)/stand dev techniques to solve it. The key is to rewrite the given probability in terms of the standard normal distribution, n(0, 1), by setting Y = X - 5 and considering how Y is distributed. From there, you can use a table or your calculator to find the value you need for X that satisfies the given probability.
  • #1
sisyphus0321
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Homework Statement


Assume x is normally distributed with a mean of 5 and standard deviation of 4. Determine value of x that solves:
P(-X<x-5<X) = .99


Homework Equations


I have been using normalCDF and inverse functions on the TI-84 to solve, and I understand how to do these without the calc as well using the standard (x-mean)/stand dev techniques.


The Attempt at a Solution


I have a good understanding of how to work the general problems as this is the last one out of 50 I have solved. The issue is how to start this one? The teacher left a mysterious hint: Distribution?
 
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  • #2
sisyphus0321 said:

Homework Statement


Assume x is normally distributed with a mean of 5 and standard deviation of 4. Determine value of x that solves:
P(-X<x-5<X) = .99
From the probability above, what you want to solve for is X, not x.
sisyphus0321 said:

Homework Equations


I have been using normalCDF and inverse functions on the TI-84 to solve, and I understand how to do these without the calc as well using the standard (x-mean)/stand dev techniques.


The Attempt at a Solution


I have a good understanding of how to work the general problems as this is the last one out of 50 I have solved. The issue is how to start this one? The teacher left a mysterious hint: Distribution?

You know that your random variable X is n(5, 4). If you let Y = X - 5, how is Y distributed? What would you need to do to get a probability involving Z, the standard normal n(0, 1) random variable? How should your original probability be rewritten so that it involves Z (and from which you can get the values you need from a table or maybe your TI?
 

FAQ: Solve Normal Distribution Homework with Mean 5, Standard Deviation 4

What is the normal distribution?

The normal distribution is a commonly used statistical distribution that follows a bell-shaped curve. It is characterized by its mean (the center of the curve) and standard deviation (the measure of how spread out the data is).

How do you solve normal distribution problems?

To solve normal distribution problems, you first need to determine the mean and standard deviation of the given data. Then, you can use the formula for the normal distribution to calculate probabilities or find specific data points. You can also use a z-score table or a calculator to assist with calculations.

What is the mean and standard deviation of the given data?

The mean of the given data is 5 and the standard deviation is 4.

What is the formula for the normal distribution?

The formula for the normal distribution is f(x) = (1/σ√2π) * e^(-1/2 * ((x-μ)/σ)^2), where μ is the mean and σ is the standard deviation.

What is a z-score and how is it related to the normal distribution?

A z-score, also known as a standard score, is a measure of how many standard deviations a data point is above or below the mean. It is calculated by subtracting the mean from the data point and dividing by the standard deviation. Z-scores are often used in normal distribution problems to determine probabilities or find specific data points.

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