Name: Finding Sigma and Mu (3.2.4) | Edexcel International AS Maths: Statistics 1 Revision Notes 2019 Membership
Brand: Save My Exams
Price: 60 GBP
Availability: OnlineOnly
Rating: 4.7 (37 reviews)

3.2.4 Finding Sigma and Mu

Finding Sigma and Mu

How do I find the mean (μ) or the standard deviation (σ) if one of them is unknown?

If the mean or standard deviation of the $X ~ N (μ, σ^{2})$ is unknown then you will need to use the standard normal distribution
You will need to use the formula
- $z = \frac{x - μ}{σ}$ or its rearranged form $x = μ + σ z$
You will be given a probability for a specific value of $x (P (X < x) = p or P (X > x) = p)$
To find the unknown parameter:
STEP 1: Sketch the normal curve
- Label the known value and the mean
STEP 2: Find the z-value for the given value of x
- Use the table of the Normal Distribution to find the value of z such that $P (Z < z) = p$ or $P (Z > z) = p$
- Make sure the direction of the inequality for Z is consistent with X
- The table gives the -value to three decimal places to avoid rounding errors
  - Use the sketch to help you decide whether your z value is positive or negative
  - You should use the 3 decimal places throughout your calculations so that your final answer can be rounded to 3 significant figures
STEP 3: Substitute the known values into $z = \frac{x - μ}{σ}$ or $x = μ + σ z$
- You will be given x and one of the parameters (μ or σ) in the question
- You will have calculated z in STEP 2
STEP 4: Solve the equation

How do I find the mean (μ) and the standard deviation (σ) if both of them are unknown?

If both of them are unknown then you will be given two probabilities for two specific values of x
The process is the same as above
- You will now be able to calculate two z-values
- You can form two equations (rearranging to the form $x = μ + σ z$ is helpful)
- You now have to solve the two equations simultaneously
- Be careful not to mix up which z-value goes with which value of $x$

Exam Tip

These questions are normally given in context so make sure you identify the key words in the question. Check whether your z-values are positive or negative and be careful with signs when rearranging.

Cookies

Up to 33% off discounts extended!

Edexcel International AS Maths: Statistics 1

Revision Notes

3.2.4 Finding Sigma and Mu

Finding Sigma and Mu

How do I find the mean (μ) or the standard deviation (σ) if one of them is unknown?

How do I find the mean (μ) and the standard deviation (σ) if both of them are unknown?

Exam Tip

Author: Daniel

Resources

Members

Company

Quick Links