6 The masses, in kilograms, of large and small sacks of grain have the distributions \(\mathrm { N } ( 53,11 )\) and \(\mathrm { N } ( 14,3 )\) respectively.
- Find the probability that the mass of a randomly chosen large sack is greater than four times the mass of a randomly chosen small sack.
- A lift can safely carry a maximum mass of 1000 kg .
Find the probability that the lift can safely carry 12 randomly chosen large sacks and 25 randomly chosen small sacks.
\(7 X\) is a random variable with distribution \(\operatorname { Po } ( 2.90 )\). A random sample of 100 values of \(X\) is taken. Find the probability that the sample mean is less than 2.88 .
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