The weight of the mature cabbage, X, is assumed to be normally distributed with expected value μ = 2.4 kg and standard deviation σ = 1.4. (a) If one chooses a cabbage head at random, what is the probability that this will: i) weigh less than 1.5 kg? ii) weigh between 2 and 2.5 kg? iii) What is the probability that the weight difference between two random selected cabbage heads must be more than 1 kg?
The weight of the mature cabbage, X, is assumed to be
(a) If one chooses a cabbage head at random, what is the probability that this will: i) weigh less than 1.5 kg? ii) weigh between 2 and 2.5 kg? iii) What is the probability that the weight difference between two random selected cabbage heads must be more than 1 kg? iv) Given that a cabbage head meets the requirement (weighs at least 1.5 kg), what is the probability that it weighs between 2 and 2.5 kg?
Cabbage heads weighing less than 1.5 kg do not meet the requirement for class l-cabbage. The farm decides to try out a new type of sort. It appears that the heads of this new type through ̊weighs more than the heads of the old type. A small trial crop of 10 plants is grown. We first assume that the 10 weight measurements Y1, Y2, . . . , Y10 are independent and normally distributed with unknown expectation μY and known standard deviation σY = 1.4. The results of the measurements are given in the table below.
b) Which estimator would you use to estimate μY ? Write down the estimator and calculate the estimate from the data in the table. Find a 90% confidence interval for μY . What will be the length of the confidence interval? How many plants did we have to have at least for the length of the confidence interval to decrease than 0.2 kg?
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