Binomial A1) On average one bowl in every 4 has lumpy porridge. If big daddy B has 6 bowls of porridge, find the probability:  (a) There are exactly 5 bowls with lumpy porridge.  (b) There are at most 1 bowl with lumpy porridge.   2) Goldilocks has nightmares on 4 nights each week on average.   a) Find the probability of her having more than 2 nights with nightmares in a week.   b) Given that she had less than 5 nightmare nights in a week, find the probability that she had only 1 nightmare night.

1st Page

Binomial B1) It is known that 60% of candidates will achieve in an examination. If 5 people sit the examination find the probability: 

(a) Exactly 3 candidates will achieve.  

(b) At least 3 candidates will achieve.   2) A drug is known to be 90% effective when it is used to cure a disease. If 20 people are given the drug then X is binomial with n = 20, = 0.9. 

a) Find the mean on the binomial distribution  

b) Find the standard deviation on the binomial distribution  

1st Page

Binomial C1) List the conditions of the binomial distribution. 

2) It is known that 18.5 % of people can turn their eyelids inside out. In a group of 20 people what is the probability that more than 1 person can turn their eyelids inside out? 

1st Page

Poisson A1) List the conditions of the Poisson distribution. 

2) In a particular marine reserve there are on average 1.25 crayfish per m2 of seafloor. In a 20m2 area what is the probability that there are 10 crayfish? 

1st Page

Poisson B1) Goldilocks breaks three chairs per hour at school because she is over weight. What is the probability that she breaks no more than four chairs and an hour. (Assume chair breakages are independent )  

2) Goldilocks has on average five tantrums per hour. What is the probability that she has at least two tantrums in a given fifteen minute interval. (Assume tantrums are independent ) 

1st Page

Poisson C1) Baby bear cries four times a week on average. What is the mean and variance of the number of times he cries and a given day.  

2) The probability that baby bears chair is not broken in a given week is 0.44

a) What is the average number of times the chair is broken in a week.

b) What is the standard deviation of the number of times the chair is broken in a week.

c) What is the probability that baby bears chair is broken twice in a week.

 

1st Page

Poisson DThe bear hunting season is five months long. On average the

bear family get angry four times a month in the bear hunting season and three times a month in the off-season.

1) What is the probability that the bear family get angry twice in the next month?

2) If the bear family did not get angry last month, what is the probability that it is the bear hunting season?

 

 

1st Page

‘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

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) =

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) =

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?

4) What percentage of mosquitoes are between 3kg and 4kg?

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?

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

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?

The mean weight of a loader scoop of coal is 1.25 tonnes and a standard deviation of 280 kg

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?

The mean weight of a loader scoop of coal is 1.25 tonnes and a standard deviation of 280 kg

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 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

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 less 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

Mixed Problems A1) Mean maximum temperature is 26°C Standard deviation = 5°C Temp measured to nearest degree. a) P(Temperature at least 30°C)     b) P(Temperature between 20 and 30°C)     c) P(Temperature between 20 and 24°C inclusive)   2) On average there are 4 frogs per litre of swamp water. What is the probability there are less than 4 frogs in a 2 litre bucket of swamp water 

1st Page

Mixed Problems A Soln1) Mean maximum temperature is 26°C Standard deviation = 5°C Temp measured to nearest degree. a) P(Temperature at least 30°C)     b) P(Temperature between 20 and 30°C)     c) P(Temperature between 20 and 24°C inclusive)   2) On average there are 4 frogs per litre of swamp water. What is the probability there are less than 4 frogs in a 2 litre bucket of swamp water 

1st Page

Mixed Problems BThe mean weight of a cake is 1.5kg with standard deviation of 0.34kgHomer weighs 120kg.

1) If Homer ate six cakes what is the mean and standard deviation of his total weight .

2) What is the probability Homer weighs over 130kg?

 

1st Page

Mixed Problems CEach day Homer is exposed to radiation for six minutes on average (variance of 1.5 minutes) Radiation exposure is considered dangerous if it is for more than five minutes per day.

1) What is the probability that Homer is exposed to dangerous levels of radiation on two consecutive days

2) What is the probability that Homer is exposed to dangerous levels of radiation for at least three days in a five day week

 

1st Page