Checking my answers 20: a) 0.2923 b) x0=256.6 c) 215g,8g d) 0.9392 The probabili

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Checking my answers
20: a) 0.2923 b) x0=256.6 c) 215g,8g d) 0.9392 The probability of a single frog weighing between 200-230g is much less than a whole sample of 25 frogs weighing between 200-230g (about 3 times less) 21: a) 0.0793 b) 0.1736 6.20. weight X, of a Giant Siamese Frog has an approximately normal distribution with a) Find the probability that a single frog weighs is between 200 and 230g. b) Find the 85th percentile of the frogs' weights. c) Let X be the average weight of 25 frogs. Find the mean and standard deviation of the mean of 215g and standard deviation of 40g X. Assume that the frogs' weights are independent. d) Approximate the probability that X is between 200 and 230g. Compare to part (a) 6.21. A process yields 10% defective items. If 200 items are randomly selected from, the process, what is the probability that the sample proportion of defectives a) exceeds 13%? b) is less than 8%?

Explanation / Answer

6.20) X is normally distributed with mean = 215 and standard deviation = 40

(a) P(200<X<230) = P((200-215)/40<X<(230-215)/40)

=P(-0.375<X<0.375)

= 1-2P(X<0.375) = 1-0.70766 = 0.29234

(b) P(X-215/40) = 1.0364 so X = 256.456

(c) mean = (25*215)/25 = 215 g

standard deviation = 40/250.5 = 8g

(d) P(200<Xbar<230) = P(-15/8<X<15/8)

= 1-2 P(X<1.875)

= 1- 0.060793 = 0.93921

The probability of a single frog weighing between 200-230g is much less than a whole sample of 25 frogs weighing between 200-230g

6.21) (a) P(X>0.13) = P(Z>1.4142) = 0.0793

(b) P(X<0.08) = P(Z< -0.94) = 0.1736

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