3.27. Problem. (Section 11.5) The following are applications of Theorem 11.6 or the Central Limit Theorem....

3.27. Problem. (Section 11.5) The following are applications of Theorem 11.6 or the Central Limit Theorem.

(a) Determine the distribution of (1/5)X₁ + (2 /5)X₂ + (2/5)X₃ if X₁, X₂ and X₃ are independent normal distributions with µ = 2 and

σ = 3.

(b) The weight (kg) of a StarBrite watermelon harvested under certain environmental conditions is normally distributed with a mean of 8.0 with standard deviation of 1.9. Suppose 24 StarBrite watermelons grown in these conditions are harvested; compute the probability that the average weight of all 24 watermelons is less than 7.8 kg/fruit

(c) A study of elementary school students reports that the mean age at which children begin reading is 5.7 years with a standard deviation of 1.1 years. If 55 elementary school students are selected at random, approximate the probability that the average age at which these 55 children begin reading is at least 6.

(d) Let the random variable X be defined as the number of pips that show up when a fair, six-sided die is rolled. The mean and standard deviation of X can be shown to be µX = 3.5 and σX = 1.71, respectively. If 100 fair, six-sided dice are rolled, aproximate the probability that the mean of number of pips on the 100 dice is less than 3.25

Expert Solution

milcah answered 10 months ago

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