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Finding Sigma and Mu (Edexcel International AS Maths: Statistics 1)
Revision Note
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 is unknown then you will need to use the standard normal distribution
- You will need to use the formula
- or its rearranged form
- You will be given a probability for a specific value of
- 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 or
- Make sure the direction of the inequality for Z is consistent with X
- The table gives the z-value to four 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 4 decimal places throughout your calculations so that your final answer can be rounded to 3 significant figures
- STEP 3: Substitute the known values into or
- 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 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
Worked example
It is known that the times, in minutes, taken by students at a school to eat their lunch can be modelled using a normal distribution with mean μ minutes and standard deviation σ minutes.
Given that 10% of students at the school take less than 12 minutes to eat their lunch and 5% of the students take more than 40 minutes to eat their lunch, find the mean and standard deviation of the time taken by the students at the school.
Examiner 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.
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