# Finding Sigma and Mu(Edexcel International A Level Maths: Statistics 1)

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Dan

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Maths

## 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
• 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.

#### 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.

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