Normal Distribution lesson 7

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Normal Distribution lesson 7 White board revision Starter Revision questions Test :First lesson next week

Mini-white board revision True or false

True or false False the total area is 1 The total area under any Normal distribution curve equals 2 The shape of a normal distribution curve has a line of symmetry True There is 50% of the area of a normal distribution between 0 and 1 standard deviation False it is about 34% Z = True

Revision questions Find (a) P(Z < 1.2) (b) P(Z < -1.4) (c) P(Z > 1.8) (d) P(-1.8 < Z < 1.2) Answers (a) 0.885 (b) 0.0808 (c) 0.0359 (d) 0.849

Revision questions 2 The lengths of components produced by a particular machine may be modelled by a normal distribution with mean 901 mm and standard deviation 2mm. Find the probability that the length of a randomly selected component will be less than 902.5mm Answer: 0.773

Revision questions 3. The weights of red gravel may be modelled by a normal distribution with mean 25.8kg and standard deviation 0.5kg. (a) Determine the probability that a randomly selected bag of red gravel will weigh : (i) less than 25kg (ii) between 25.5kg and 26.5 kg (b) Determine the weight exceeded by 75% of bags Answer (a) (i) 0.0548 (a) (ii) 0.645 (b) 25.48

4 The weight of a particular variety of orange is normally distributed with a mean of 155 grams and a standard deviation of 10 grams. (a) Find the probability of oranges having weights' between 145 and 165 grams (b) Find the weight exceeded by 67% of the oranges. Answers (a) 68.3 % (b) 151 grams

5 The time taken from entering a self service canteen at lunch time to completing the purchase of food can be modelled by a normal distribution with mean 245 seconds and standard deviation 40 seconds. (a) Find the probability that it will take Sheila between 200 and 300 seconds from entering the canteen to completing her purchase of food. (b) Sheila agrees to purchase her food prior to meeting Kofi at the canteen at 1.00pm. Find how many seconds before 1.00pm she should enter the canteen to have a probability of 0.98 of meeting Kofi on time. Answers (a) 0.787 (b) 327 seconds

6. The weights of hen's eggs are normally distributed with a mean of 65 grams and a standard deviation of 10 grams. Eggs whose weights are less than 56.5 grams are classified as small. (a) Calculate the proportion of eggs that are classified as small Those eggs which are not classified as small are classified as median or large in equal proportions. (b) Calculate the weight above which eggs are classified as large Answers: (a) 19.8% (b) 67.5grams