Question

1.The weight W of the 60cm×60cm patio stones sold by Delightful Gardens is a normally distributed random variable with mean and standard deviation equal to 22.6kgs and 0.8kgs respectively. (a) Mr.Chancey buys one of this type of patio stones in order to replace a similar one that was broken in his backyard. What is the probability that the new patio stone will weigh less than 22.0kgs? Draw the probability density function of W, neatly and clearly, and indicate the area that corresponds to this probability. (b) Compute (i) the lower quartile and (ii) the upper decile of the probability distribution of W. Explain, clearly and neatly, the meaning of these quantities. (c) Let M represent the mean weight of a random sample of 16 patio stones. (i) Find the mean and standard deviation of M. (ii) Write down the probability density function of W and M. (iii) Draw the probability density function of W and M on the same diagram. (iv) Compute the probability that M exceeds 22.5kgs. (d) Let T be the sum of the weights of 25 patio stones. Find E(T) and Var(T). Then compute the probability that T exceeds 560.0kgs. Draw the probability density function of T, neatly and clearly, and indicate the area that corresponds to this probability.

          1.The weight W of the 60cm×60cm patio stones sold by Delightful Gardens is a normally distributed random variable with mean and standard deviation equal to 22.6kgs and 0.8kgs respectively.
(a) Mr.Chancey buys one of this type of patio stones in order to replace a similar one that was broken in his backyard. What is the probability that the new patio stone will weigh less than 22.0kgs? Draw the probability density function of W, neatly and clearly, and indicate the area that corresponds to this probability.
(b) Compute (i) the lower quartile and (ii) the upper decile of the probability distribution of W. Explain, clearly and neatly, the meaning of these quantities.
(c) Let M represent the mean weight of a random sample of 16 patio stones. (i) Find the mean and standard deviation of M. (ii) Write down the probability density function of W and M. (iii) Draw the probability density function of W and M on the same diagram. (iv) Compute the probability that M exceeds 22.5kgs.
(d) Let T be the sum of the weights of 25 patio stones. Find E(T) and Var(T). Then compute the probability that T exceeds 560.0kgs. Draw the probability density function of T, neatly and clearly, and indicate the area that corresponds to this probability.

1.The weight W of the 60cm×60cm patio stones sold by Delightful Gardens is a normally distributed random variable with mean and standard deviation equal to 22.6kgs and 0.8kgs respectively.
(a) Mr.Chancey buys one of this type of patio stones in order to replace a similar one that was broken in his backyard. What is the probability that the new patio stone will weigh less than 22.0kgs? Draw the probability density function of W, neatly and clearly, and indicate the area that corresponds to this probability.
(b) Compute (i) the lower quartile and (ii) the upper decile of the probability distribution of W. Explain, clearly and neatly, the meaning of these quantities.
(c) Let M represent the mean weight of a random sample of 16 patio stones. (i) Find the mean and standard deviation of M. (ii) Write down the probability density function of W and M. (iii) Draw the probability density function of W and M on the same diagram. (iv) Compute the probability that M exceeds 22.5kgs.
(d) Let T be the sum of the weights of 25 patio stones. Find E(T) and Var(T). Then compute the probability that T exceeds 560.0kgs. Draw the probability density function of T, neatly and clearly, and indicate the area that corresponds to this probability.

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