Question

Problem 1: [9 points] Weights X of female cats of a certain breed are normally distributed with mean ? = 4.1 kg and a standard deviation of ? = 0.6 kg. (a) What proportion of female cats have weights between 3.7 and 4.4 kg? [1] (b) A certain female cat has a weight that is 0.5 standard deviation (0.5?) above the mean. What proportion of female cats are heavier than this one? [1] (c) Find the 80th percentile of the female cats weights and interpret it. [3] (d) What is the likelihood that a randomly chosen female cat weights more than 4.5 kg? [1] (e) Six female cats are chosen at random. Their weights are independent from one another. Let Y be the number out of those 6 whose weight is more than 4.5 kg. (i) What is the distribution of X? Give its expression. [2] (ii) Find the probability that exactly two have a weight more than 4.5 kg. [1]

          Problem 1: [9 points] Weights X of female cats of a certain breed are normally distributed with mean ? = 4.1 kg and a standard deviation of ? = 0.6 kg.
(a) What proportion of female cats have weights between 3.7 and 4.4 kg? [1]
(b) A certain female cat has a weight that is 0.5 standard deviation (0.5?) above the mean. What proportion of female cats are heavier than this one? [1]
(c) Find the 80th percentile of the female cats weights and interpret it. [3]
(d) What is the likelihood that a randomly chosen female cat weights more than 4.5 kg? [1]
(e) Six female cats are chosen at random. Their weights are independent from one another. Let Y be the number out of those 6 whose weight is more than 4.5 kg.
(i) What is the distribution of X? Give its expression. [2]
(ii) Find the probability that exactly two have a weight more than 4.5 kg. [1]

Problem 1: [9 points] Weights X of female cats of a certain breed are normally distributed with mean ? = 4.1 kg and a standard deviation of ? = 0.6 kg.
(a) What proportion of female cats have weights between 3.7 and 4.4 kg? [1]
(b) A certain female cat has a weight that is 0.5 standard deviation (0.5?) above the mean. What proportion of female cats are heavier than this one? [1]
(c) Find the 80th percentile of the female cats weights and interpret it. [3]
(d) What is the likelihood that a randomly chosen female cat weights more than 4.5 kg? [1]
(e) Six female cats are chosen at random. Their weights are independent from one another. Let Y be the number out of those 6 whose weight is more than 4.5 kg.
(i) What is the distribution of X? Give its expression. [2]
(ii) Find the probability that exactly two have a weight more than 4.5 kg. [1]

Added by Ashley H.

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