RI Normal Distribution Tutorial Q4
RI Normal Distribution Tutorial Q4
11 marks
The weights of a randomly chosen \(10\)-month old male baby, \(X\) kg, and a randomly chosen female baby, \(Y\) kg, are modelled as having independent normal distributions with means and standard deviations as shown in the table.
| Mean | Standard Deviation | |
|---|---|---|
| \(X\) | \(9.2\) | \(0.8\) |
| \(Y\) | \(8.5\) | \(0.5\) |
- Find the probability that the difference between thrice the weight of a male baby and the total weight of five female babies does not exceed \(10\) kg.[3]
- Find the probability that the mean weight of four randomly chosen male babies is at least \(0.5\) kg more than the mean weight of three randomly chosen female babies.[3]
- The probability that the total weight of two males and one female babies is less than \(m\) kg is at least \(0.9\). Find the least integral value of \(m\).[2]
- Four female babies are selected at random. Calculate the probability that exactly two of them weigh more than \(9\) kg and exactly one of them weighs less than \(8\) kg.[3]
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Answer:(i) \(0.0321\) (ii) \(0.657\) (iii) \(m=29\) (iv) \(0.0327\)
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