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Normal Distribution Starters Starter AStarter A Starter A Solns (z values)Starter A Solns Starter BStarter B Starter B Solns A Starter B Solns BStarter.

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Presentation on theme: "Normal Distribution Starters Starter AStarter A Starter A Solns (z values)Starter A Solns Starter BStarter B Starter B Solns A Starter B Solns BStarter."— Presentation transcript:

1 Normal Distribution Starters Starter AStarter A Starter A Solns (z values)Starter A Solns Starter BStarter B Starter B Solns A Starter B Solns BStarter B Solns AStarter B Solns B Starter CStarter C Starter C: Solns 1 Starter C: Solns 2Starter C: Solns 1Starter C: Solns 2 Starter DStarter D Starter D: Solns 1 Starter D: Solns 2Starter D: Solns 1Starter D: Solns 2 Starter EStarter E Starter E: Solns 1 Starter E: Solns 2Starter E: Solns 1Starter E: Solns 2 Starter FStarter F Starter F: Solns 1 Starter F: Solns 2Starter F: Solns 1Starter F: Solns 2 Starter GStarter G Starter G: Solns 1 Starter G: Solns 2Starter G: Solns 1Starter G: Solns 2 Starter HStarter H Starter H Solns (inverse z values)Starter H Solns Starter IStarter I Starter I: Solns 1 Starter I: Solns 2Starter I: Solns 1Starter I: Solns 2

2 ‘Z’ values 0 z Look up these ‘z’ values to find the corresponding probabilities 1) P(0 < z < 1.4) =2) P(0 < z < 2.04) = 3) P(0 < z < 1.55) =4) P(0 < z < 2.125) = 5) P( < z < 0) =6) P(-2.44 < z < 2.44) = 7) P(-0.85 < z < 1.646) =8) P( z < 2.048) = 9) P(1.955 < z < 2.044) =10) P( z < ) = 1 st Page

3 ‘Z’ value Solutions 0 z Look up these ‘z’ values to find the corresponding probabilities 1) P(0 < z < 1.4) =2) P(0 < z < 2.04) = 3) P(0 < z < 1.55) =4) P(0 < z < 2.125) = 5) P( < z < 0) =6) P(-2.44 < z < 2.44) = 7) P(-0.85 < z < 1.646) =8) P( z < 2.048) = 9) P(1.955 < z < 2.044) =10) P( z < ) = 1 st Page

4 Starter B 240mm A salmon farm water tank contains fish with a Mean length of 240mm Calculate the probability of the following (Std dev = 15mm) 1) P(A fish is between 240 and 250mm long) = 2) P(A fish is between 210 and 260mm long) = 3) P(A fish is less than 254mm long) = 4) P(A fish is less than 220mm long) = 5) P(A fish is between 255 and 265mm long) = 1 st Page

5 Starter B Solns 1 240mm A salmon farm water tank contains fish with a Mean length of 240mm Calculate the probability of the following (Std dev = 15mm) 1) P(A fish is between 240 and 250mm long) = 2) P(A fish is between 210 and 260mm long) = 3) P(A fish is less than 254mm long) = 1 st Page

6 Starter B Solns 2 240mm A salmon farm water tank contains fish with a Mean length of 240mm Calculate the probability of the following (Std dev = 15mm) 4) P(A fish is less than 220mm long) = 5) P(A fish is between 255 and 265mm long) = 1 st Page

7 Starter C 4.8kg A west coast population of mosquitoes have a Mean weight of 4.8kg Calculate the probability of the following (Std dev = 0.6kg) 5) What percentage of mosquitoes are under 5.5kg? 1 st Page 1) What is the probability a mosquito is between 4.8kg and 5.8kg? 2) What percentage of mosquitoes are between 4kg and 5kg? 3) Out of a sample of 120 mosquitoes, how many would be over 6kg? 4) What percentage of mosquitoes are between 3kg and 4kg?

8 Starter C: Solns 1 4.8kg A west coast population of mosquitoes have a Mean weight of 4.8kg Calculate the probability of the following (Std dev = 0.6kg) 1 st Page 1) What is the probability a mosquito is between 4.8kg and 5.8kg? 2) What percentage of mosquitoes are between 4kg and 5kg? 4.8kg

9 Starter C: Solns 2 4.8kg A west coast population of mosquitoes have a Mean weight of 4.8kg Calculate the probability of the following (Std dev = 0.6kg) 5) What percentage of mosquitoes are under 5.5kg? 1 st Page 3) Out of a sample of 120 mosquitoes, how many would be over 6kg? 4) What percentage of mosquitoes are between 3kg and 4kg? 4.8kg

10 Starter D 1 st Page 3.6g 5) What percentage of flies are under 2.5g 1) What is the probability a fly is between 3.6g and 5.8g? 2) What percentage of flies are between 3g and 5g? 3) Out of a sample of 40 flies, how many would be under 4g? 4) What percentage of flies are between 2g and 3g? A room contains flies with a Mean weight of 3.6g and a Standard Deviation of 0.64kg

11 Starter D: Solns 1 1 st Page 3.6g 1) What is the probability a fly is between 3.6g and 5.8g? 2) What percentage of flies are between 3g and 5g? A room contains flies with a Mean weight of 3.6g and a Standard Deviation of 0.64kg 3.6g

12 Starter D: Solns 2 1 st Page 3.6g 5) What percentage of flies are under 2.5g 3) Out of a sample of 40 flies, how many would be under 4g? 4) What percentage of flies are between 2g and 3g? A room contains flies with a Mean weight of 3.6g and a Standard Deviation of 0.64kg 3.6g

13 Starter E 1 st Page 1.25t 5) What percentage of scoops are between 1 tonne and 2 tonnes 1) What percentage of scoops are between 1.3 and 1.5 tonnes? 2) What percentage of scoops are less than 1 tonne? 3) Out of a sample of 500 scoops, how many would be over 1.4 tonnes? 4) What percentage of scoops are more than 1.6 tonnes? The mean weight of a loader scoop of coal is 1.25 tonnes and a standard deviation of 280 kg

14 Starter E: Solns 1 1 st Page 1.25t 1) What percentage of scoops are between 1.3 and 1.5 tonnes? 2) What percentage of scoops are less than 1 tonne? The mean weight of a loader scoop of coal is 1.25 tonnes and a standard deviation of 280 kg 1.25t

15 Starter E: Solns 2 1 st Page 1.25t 5) What percentage of scoops are between 1 tonne and 2 tonnes 3) Out of a sample of 500 scoops, how many would be over 1.4 tonnes? 4) What percentage of scoops are more than 1.6 tonnes? The mean weight of a loader scoop of coal is 1.25 tonnes and a standard deviation of 280 kg 1.25t

16 Starter F 1 st Page 4.6kg 5) What is the probability he does not eat between 3.5 & 5 kg of glue paste? 1) How many days in November will Ralph eat less than 5.5kg of glue paste? 2) What percentage of days does he eat less than 4kg of glue paste? 3) Ralph vomits when he eats more than 6kg of glue in a day. What is the chance of this happening? 4) What percentage of days does he eat between 4.2kg and 5kg of glue? The weight of glue paste Ralph eats in a day is normally distributed with a mean of 4.6kg & standard deviation of 1.3kg

17 Starter F: Solns 1 1 st Page 4.6kg 1) How many days in November will Ralph eat less than 5.5kg of glue paste? 2) What percentage of days does he eat less than 4kg of glue paste? The weight of glue paste Ralph eats in a day is normally distributed with a mean of 4.6kg & standard deviation of 1.3kg 4.6kg

18 Starter F: Solns 2 1 st Page 4.6kg 5) What is the probability he does not eat between 3.5 & 5 kg of glue paste? 3) Ralph vomits when he eats more than 6kg of glue in a day. What is the chance of this happening? 4) What percentage of days does he eat between 4.2kg and 5kg of glue? The weight of glue paste Ralph eats in a day is normally distributed with a mean of 4.6kg & standard deviation of 1.3kg 4.6kg

19 Starter G 1 st Page 10.4kg 5) 90% of hammers weigh more than what weight? 1) What percentage of the hammers weigh less than 8kg? 2) What is the probability a hammer weighs between 11kg & 14kg? 3) Scratchy’s head splits open if the hammer is more than 15kg. What is the chance of this happening? 4) A truck is loaded with 200 hammers. How many of these would be 12kg or less? Itchy & Scratchy have a hammer collection which is normally distributed with a mean of 10.4 kg & standard deviation of 2.3kg

20 Starter G: Solns 1 1 st Page 10.4kg 1) What percentage of the hammers weigh less than 8kg? 2) What is the probability a hammer weighs between 11kg & 14kg? Itchy & Scratchy have a hammer collection which is normally distributed with a mean of 10.4 kg & standard deviation of 2.3kg) 10.4kg

21 Starter G: Solns 2 1 st Page 10.4kg 5) 90% of hammers weigh more than what weight? 3) Scratchy’s head splits open if the hammer is more than 15kg. What is the chance of this happening? 4) A truck is loaded with 200 hammers. How many of these would be 12kg or less? Itchy & Scratchy have a hammer collection which is normally distributed with a mean of 10.4 kg & standard deviation of 2.3kg) 10.4kg

22 Inverse ‘Z’ values 0 z Look up these probabilities to find the corresponding ‘z’ values 1) 2) 5) 6) 7) 8) 1 st Page 3) 4)

23 Inverse ‘Z’ values: Solns 0 z Look up these probabilities to find the corresponding ‘z’ values 1) 2) 5) 6) 7) 8) 1 st Page 3) 4)

24 Starter I 1 st Page 120mL 5) The middle 80% of blood losses are between what two amounts? 1) What is the probability his blood loss is than 100mL? 2) 80% of the time his blood loss is more then ‘M’ mL. Find the value of ‘M’ 3) Kenny passes out when his blood loss is too much. This happens 5% of the time. What is the maximum amount of blood loss Kenny can sustain? 4) 30% of the time Kenny is not concerned by his blood loss? What is his blood loss when he starts to be concerned? Kenny is practicing to be in a William Tell play. He suffers some blood loss which is normally distributed with a mean of 120mL & standard deviation of 14mL

25 Starter I: Solns 1 1 st Page 120mL 1) What is the probability his blood loss is than 100mL? 2) 80% of the time his blood loss is more then ‘M’ mL. Find the value of ‘M’ 3) Kenny passes out when his blood loss is too much. This happens 5% of the time. What is the maximum amount of blood loss Kenny can sustain? Kenny is practicing to be in a William Tell play. He suffers some blood loss which is normally distributed with a mean of 120mL & standard deviation of 14mL 120mL

26 Starter I: Solns 2 1 st Page 120mL 5) The middle 80% of blood losses are between what two amounts? 4) 30% of the time Kenny is not concerned by his blood loss? What is his blood loss when he starts to be concerned? Kenny is practicing to be in a William Tell play. He suffers some blood loss which is normally distributed with a mean of 120mL & standard deviation of 14mL Lucky Kenny is not involved in the knife catching competition! 120mL


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