additionalmathematicsadditionalmath ematicsadditionalmathematicsadditio nalmathematicsadditionalmathematic sadditionalmathematicsadditionalmat

Transcription

1 additionalmathematicsadditionalmath ematicsadditionalmathematicsadditio nalmathematicsadditionalmathematic sadditionalmathematicsadditionalmat PROBABILTY DISTRIBUTION hematicsadditionalmathematicsadditi [REINFORCEMENT] onalmathematicsadditionalmathemati Name csadditionalmathematicsadditionalma... thematicsadditionalmathematicsadditi onalmathematicsadditionalmathemati csadditionalmathematicsadditionalma thematicsadditionalmathematicsadditi onalmathematicsadditionalmathemati csadditionalmathematicsadditionalma thematicsadditionalmathematicsadditi onalmathematicsadditionalmathemati csadditionalmathematicsadditionalma

2 Probability Distributions 8.1 Binomial distributions 1.Find the following probabilities: Ex. p=0.4 n=10 r=6 P( x r) C p (1 p) P( x=6 ) = n r n r r (a) p=0.7 n=8 r=5 P( x r) C p (1 p) P( x=5 ) = n r n r r (b) p=0.2 n=5 r=3 P( x r) C p (1 p) P( x=3 ) = n r n r r (c) p=0.3 n=12 r=8 P( x r) C p (1 p) P( x=8 ) = n r n r r 2. Ex. The probability that Ali late for school is 0.1. find the probability that Ali late for school for 2 out of 5 school days. (a)the probability that Ali late for school is 0.2. find the probability that Ali late for school for 3 out of 5 school days. (b)the probability that Ali wins in a game is 0.7. find the probability that Ali will win 4 out of 6 games played. (c) The probability that Ali wins in a game is 0.8. find the probability that Ali will win 5 out of 7 games played.

3 8.2 Mean, variance and standard deviation of a Binomial Distributions 2 3. Find the following values of,, and Ex. n=40, p=1/4 (a) n=60, p= 1/2 n=100, p=1/5 n=60, p=1/3 4. Ex. A die is tossed 100 times. Find the mean and the standard deviation of getting the number 5 (a)a die is tossed 400 times. Find the mean and the standard deviation of getting the number 6 (b)a die is tossed 500 times. Find the mean and the standard deviation of getting the number 1 or 3 (c)a die is tossed 200 times. Find the mean and the standard deviation of getting the number an even number. 5. Ex. A piece is tossed 600 times. Find the mean, variance and standard deviation of getting head (a) A piece is tossed 500 times. Find the mean, variance and standard deviation of getting tail (b)a box contains 2 white cards, 5 blue cards and 3 yellow cards. A card is picked randomly from the box with replacement. This process is repeated 100 times. Find the mean and standard deviation of getting a white card. (c)a box contains 4 white cards, 6 blue cards and 2 yellow cards. A card is picked randomly from the box with replacement. This process is repeated 400 times. Find the mean and standard deviation of getting a white card.

4 8.3 Normal Distributions Find the following probability 6.Ex. P( z 0.3 ) (a) P( z 0.8 ) (b) P( z 1.3 ) (c) P( z 2.3 ) 7. Ex P( z 0.6) (a) P( z 0.9) (b) P( z 1.2) (c) P( z 0.75) 8. Ex. P( z 0.8 ) (a) P( z 1.2 ) (b) P( z 2.4 ) (c) P( z 0.85 )

5 9. Ex. Pz ( 0.5) (a) Pz ( 0.9) (b) Pz ( 1.2) (c) Pz ( 0.85) 10. Ex. P(0.2 z 1.2) (a) P(0.3 z 0.9) (b) P(0.65 z 1.4) (c) P(0.5 z 1.5) 11.Ex. P( 0.5 z 0.2 ) (a) P( 1.3 z 0.5 ) (b) P( 0.9 z 0.4 ) (c) P( 1.5 z 0.8 ) 12. Ex. P( 0.5 z 0.2 ) (b) P( 0.8 z 1.2 ) (c) P( 1.4 z 0.25 ) (d) P( 1.2 z 1.2 )

6 8.4 Standardised variable, Z ( z score) 13. Ex. The mean and standard deviation of a normal distribution are 8 and 2 respectively. Find the z-score if x=15 (a) The mean and standard deviation of a normal distribution are 10 and 4 respectively. Find the z-score if x=14 (b) The mean and standard deviation of a normal distribution are 75 and 25 respectively. Find the z-score if x=115 (c) The mean and standard deviation of a normal distribution are 100 and 40 respectively. Find the z-score if x= The mean and variance of a normal distribution are 30 and 400. Find the z-score if x = 28.5 (a)the mean and variance of a normal distribution are 12 and 1. Find the z-score if x = 10.5 (b)the mean and variance of a normal distribution are 40 and 225. Find the z-score if x = 35 (c)the mean and variance of a normal distribution are 60 and 144. Find the z-score if x = 48

7 8.5 Determine the probability of an event 15. EX The mass of pupils in a school have a normal distribution with mean 50 kg and a standard deviation of 8 kg. A pupil is chosen at random, calculate the probability that his mass is more than 60 kg (a) The height of pupils in a school have a normal distribution with mean 150 kg and a standard deviation of 10 kg. A pupil is chosen at random, calculate the probability that his mass is more than 155 kg (b) The scores of pupils in a school have a normal distribution with mean 60 and a standard deviation of 16. A pupil is chosen at random, calculate the probability that his mass is less than 56 (c)the scores of pupils in a school have a normal distribution with mean 60 and a standard deviation of 10. A pupil is chosen at random, calculate the probability that his mass is less than The mass of the fish in a pond have a normal distribution with mean 7 50 g and a standard deviation of 200g. A fish is chosen at random, calculate the probability that its mass is between 600 g and 1000g. (a) The mass of the fish in a pond have a normal distribution with mean 40 g and a standard deviation of 8g. A fish is chosen at random, calculate the probability that its mass is between 36 g and 48g (b) The mass of the durians from an orchard has a normal distribution with mean 2.50 kg and a standard deviation of 1.4 kg. A durian is chosen at random, calculate the probability that its mass is between 2.0 kg and 2.8 kg (c)the mass of the durians from an orchard has a normal distribution with mean 2.4 kg and a standard deviation of kg. A durian is chosen at random, calculate the probability that its mass is between 2.0 kg and 2.8 kg

8