- Albert uses scales in his kitchen to weigh some fruit.
The random variable \(D\) represents, in grams, the weight of the fruit given by the scales minus the true weight of the fruit. The random variable \(D\) is uniformly distributed over the interval \([ - 2.5,2.5 ]\)
- Specify the probability density function of \(D\)
- Find the standard deviation of \(D\)
Albert weighs a banana on the scales.
- Write down the probability that the weight given by the scales equals the true weight of the banana.
- Find the probability that the weight given by the scales is within 1 gram of the banana's true weight.
Albert weighs 10 bananas on the scales, one at a time.
- Find the probability that the weight given by the scales is within 1 gram of the true weight for at least 6 of the bananas.