(Solved): (a) For the normal distribution shown in Figure 1, find approximate values fo ...

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(a) For the normal distribution shown in Figure 1, find approximate values for its mean and standard deviation. Explain how you obtained your answers. \( [3] \) (b) The normal distribution of a variable \( x \) has mean \( \mu=10 \) and standard deviation \( \sigma=5 \). (i) Sketch this distribution, showing the key features of the distribution on the sketch. You may produce this sketch by hand or using drawing tools on a computer. The sketch should not be generated by a computer, e.g. using a graphing, statistical or spreadsheet package. Explain and show any calculations used to determine the key features of the distribution. (ii) Write down the formula for \( z \) that converts each value of the variable \( x \) in part (b) (i) so that \( z \) follows a standard normal distribution. Your answer should contain both the general formula and the specific formula for this example. (iii) Calculate the value of \( z \) corresponding to \( x=7 \). (iv) Interpret the value of \( z \) in terms of the number of standard deviations the value \( x=7 \) lies above or below its mean. [3]