SAJC Check your understanding_Normal Distribution_Teacher

Check your Understanding (Normal Distribution) Section 1: Probability 1. Drill & Practice Given that   2~ N 120,2X . Find (i)  P 119X  (ii)  P 125X  (iii) P(118 121)X Answers (i) 0.691 (ii) 0.215 (iii) 0.533 (i)  P 119 0.691X  ] (ii)  P 125 0.994X  (iii) P(118 121) 0.533X   2. YJC Promo 8865/2018/Q7 In a national park, it is known that the lengths of garden snails are normally distributed with mean 3.42 cm and standard deviation 1.10 cm. It is found that 70% of them measure less than 4.0 cm and 80% measure at least 2.5 cm. (ii) Find the probability that the length of a randomly selected garden snail is within ± 0.3 cm of the mean length. [2] Answers (ii) 0.215 YJC Promo 8865/2018/Q7 (ii)     2 2 ~ N 3.42, 1.10 or ~ N 3.42417, 1.09808 G G  P 0.3 0.3 G      3.42 0.3 3.42 0.3 0.214937 0.215 (to 3 s.f.) G       [or 0.21530] 3. JPJC JC1 Promo 8865/2019/Q7 A butcher sells chicken in two different cuts, leg and wing. The masses, in kilograms, of these two cuts have independent normal distributions. The means and standard deviations of these distributions, and the selling prices, in $ per kilogram, are shown in the following table. Mean Standard deviation Selling price Leg 0.35 0.010 12 Wing 0.09 0.003 9 Stating clearly the mean and variance of all distributions that you use, find the probability that

(i) the mass of a randomly chosen wing is within 0.005 kg of the mean mass of wings, [2] (ii) out of 3 randomly chosen wings, exactly one is less than 0.088 kg, exactly one is more than 0.09 kg and exactly one is between 0.088 kg and 0.09 kg, [3] JPJC JC1 Promo 8865/2019/Q7 (Solutions) Let L and W denote the mass of a leg and wing respectively. 2 2 ~ (0.35,0.010 ) ~ (0.09,0.003 ) LN WN (i) P(0.085 0.095) 0.90442 0.904W    (ii) Required probability = P( 0.088) P( 0.09) P(0.088 0.09) 3! (0.25249) (0.5) (0.24751) 3! 0.18748 0.187 W W W            4. MI Prelim 8865/2018/Q9 In this question you should state clearly the values of the parame ters of any normal distribution you use. In a particular stall, the masses, in kilograms, of a particular type of fish called groupers have a mean mass of 0.5 kg and standard deviation 0.0182 kg. (ii) Find the probability that the mass of a randomly chosen grouper is within 0.01 kg of the mean mass of groupers in the stall. [2] Answers (ii) 0.417 MI Prelim 8865/2018/Q9 (ii) Let G be the random variable denoting the mass, in grams, of a randomly selected groupers.   2~ N 0.5, 0.0182G    P 0.5 0.01 0.5 0.01 P 0.49 0.51 0.417 (3 sf) GG        5. PJC Prelim 8865/2018/Q12 The masses of oranges sold by a supermarket have a normal distribution. The mean and standard