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
Find the probability that a particular value generated by the computer program is less than 37
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
Find the value of \(m\), giving your answer to 2 decimal places.
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.
Find the probability that at least one of these values is negative.