Jia writes a computer program that randomly generates values from a normal distribution. He sets the mean as 40 and the standard deviation as 2.4 (a) Find the probability that a particular value generated by the computer program is less than 37 (3) Jia changes the mean to $$\(m\)$$ but leaves the standard deviation as 2.4 The computer program then randomly generates 2 independent values from this normal distribution. The probability that both of these values are greater than 32 is 0.16 (b) Find the value of $$\(m\)$$, giving your answer to 2 decimal places. (4) Jia now changes the mean to 4 and the standard deviation to 8 The computer program then randomly generates 5 independent values from this normal distribution. (c) Find the probability that at least one of these values is negative. (4)

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