1. Normal Distribution Starters
Starter A Starter A Solns (z values)
Starter B Starter B Solns A Starter B Solns B
Starter C Starter C: Solns 1 Starter C: Solns 2
Starter D Starter D: Solns 1 Starter D: Solns 2
Starter E Starter E: Solns 1 Starter E: Solns 2
Starter F Starter F: Solns 1 Starter F: Solns 2
Starter G Starter G: Solns 1 Starter G: Solns 2
Starter H Starter H Solns (inverse z values)
Starter I Starter I: Solns 1 Starter I: Solns 2

2. 1st Page
‘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 < ) =

3. ‘Z’ value Solutions 1st Page
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 < ) =

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

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

6. 1st Page
Starter B Solns 2
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) =
240mm
5) P(A fish is between 255 and 265mm long) =
240mm

7. 1st Page
Starter C
A west coast population of mosquitoes have a Mean weight of 4.8kg
Calculate the probability of the following (Std dev = 0.6kg)
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?
4.8kg
5) What percentage of mosquitoes are under 5.5kg?

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

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

10. Starter D 1st Page A room contains flies with a Mean weight of 3.6g
and a Standard Deviation of 0.64kg
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?
3.6g
5) What percentage of flies are under 2.5g

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

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

13. 1st Page
Starter E
The mean weight of a loader scoop of coal is 1.25 tonnes
and a standard deviation of 280 kg
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?
1.25t
5) What percentage of scoops are between 1 tonne and 2 tonnes

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

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

16. 1st Page
Starter F
The weight of glue paste Ralph eats in a day is normally
distributed with a mean of 4.6kg & standard deviation of 1.3kg
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?
4.6kg
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?
5) What is the probability he does not eat
between 3.5 & 5 kg of glue paste?

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

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

19. 1st Page
Starter G
Itchy & Scratchy have a hammer collection which is normally
distributed with a mean of 10.4 kg & standard deviation of 2.3kg
1) What percentage of the hammers weigh less than 8kg?
10.4kg
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?
5) 90% of hammers weigh more than what weight?

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

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

22. Inverse ‘Z’ values 1st Page 0 z
Look up these probabilities to find the corresponding ‘z’ values
1) )
0.4
0.3
3) )
0.85
0.45
5) )
0.65
0.08
7) )
0.12
0.02

23. Inverse ‘Z’ values: Solns
1st Page
Inverse ‘Z’ values: Solns
0 z
Look up these probabilities to find the corresponding ‘z’ values
1) )
0.4
0.3
3) )
0.85
0.45
5) )
0.65
0.08
7) )
0.12
0.02

24. 1st Page
Starter I
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
1) What is the probability his blood loss is than 100mL?
120mL
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?
5) The middle 80% of blood losses are between what two amounts?

25. Starter I: Solns 1 1st Page
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
1) What is the probability his blood loss is than 100mL?
120mL
2) 80% of the time his blood loss is more then ‘M’ mL. Find the value of ‘M’
120mL
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?
120mL

26. Starter I: Solns 2 1st Page
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
4) 30% of the time Kenny is not concerned by his blood loss?
What is his blood loss when he starts to be concerned?
120mL
5) The middle 80% of blood losses are between what two amounts?
120mL
Lucky Kenny is not involved in the knife catching competition!