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

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

‘Z’ values0 zLook 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(-0.844 < 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 < -2.111) =

1st Page

‘Z’ value Solutions0 zLook 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(-0.844 < 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 < -2.111) =

1st Page

Starter B

240mm

240mm

240mm

240mm

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) =


3) P(A fish is less than 254mm long) =



1st Page

http://images.google.co.nz/url?q=http://www.juliangibson.com/images/thumbnails/cartoon/fish01.jpg

Starter B Solns 1

240mm

240mm

240mm





1st Page


Starter B Solns 2

240mm

240mm




1st Page


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?

1st 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?


http://www.ci.boulder.co.us/openspace/images_kids/Mosquito_cartoon.gif

Starter C: Solns 1

4.8kg


1st Page

1) What is the probability a mosquito is between 4.8kg and 5.8kg?


4.8kg


Starter C: Solns 2

4.8kg


5) What percentage of mosquitoes are under 5.5kg?

1st Page

3) Out of a sample of 120 mosquitoes, how many would be over 6kg?


4.8kg

4.8kg


Starter D1st Page

3.6g5) 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?


A room contains flies with a Mean weight of 3.6g and a Standard Deviation of 0.64kg

Starter D: Solns 11st Page

3.6g

1) What is the probability a fly is between 3.6g and 5.8g?



3.6g

Starter D: Solns 21st 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?



3.6g

3.6g

Starter E1st 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

Starter E: Solns 11st 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?


1.25t

Starter E: Solns 21st 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?


1.25t

1.25t

Starter F1st 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

Starter F: Solns 11st 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?


4.6kg

Starter F: Solns 21st 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?


4.6kg

4.6kg

Starter G1st 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

Starter G: Solns 11st 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

Starter G: Solns 21st 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

10.4kg

Inverse ‘Z’ values0 zLook up these probabilities to find the corresponding ‘z’ values

1) 2)

5) 6)

7) 8)

1st Page

3) 4)0.85

0.65

0.3 0.4

0.45

0.08

0.020.12

Inverse ‘Z’ values: Solns0 zLook up these probabilities to find the corresponding ‘z’ values

1) 2)

5) 6)

7) 8)

1st Page

3) 4)0.85

0.65

0.3 0.4

0.45

0.08

0.020.12

Starter I1st 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

Starter I: Solns 11st 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?


120mL

120mL

Starter I: Solns 21st 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?


Lucky Kenny is not involved in the knife catching competition!

120mL

Documents

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