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How did STATISTICS 1 go?

What do you think?

  • Total voters
    98
  • Poll closed .
U

unkidd

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randomcod said:
I made the silliest mistake on the permutations question for 5p2. I multiplied it by 5 instead of 3 (so many 5s made me write it even though I knew I had to multiply by 3, didn't even notice). Also taking off marks which I have not identified as error,s, you know, we all have those small mistakes we think are correct and are only worth 1 mark, such as rounding to wrong amount of s.f.'s, so I'm deducting marks off myself to get in the worst case. If that makes any sense lol.
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i was so tired that i accidently did 5!*3 instead of 5P2*3
 
Mohammad Farzanullah

Mohammad Farzanullah

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Kamihus said:
Q1 [4 marks]
n=19 probability of success=0.12, find fewer than 4 so apply binomial with 0,1,2 and 3
Ans: 0.813

Q2 [4 marks]
Group A was of 7, Group B was of 2, Group C was of 2. Choose 5 and at least 1 from each group.
Possibilities:
3 from A and 1 from B and 1 from C. 7C3*2C1*2C1=140
2 from A and 2 from B and 1 from C. 7C2*2C2*2C1=42
2 from A and 1 from B and 2 from C. 7C2*2C1*2C2-42
1 from A and 2 from B and 2 from C. 7C1*2C2*2C2=7
Add them.
Ans: 231

Q3 (i) [3 marks] (ii) [2 marks]
Roger had a probability of winning first set=0.6
Roger had a probability of winning second set if he had won the first set=0.7
Roger had a probability of winning second set if he lost the first set=0.25
Match would end when any player wins 2 sets and match cannot be drawn and Andy was the other player.

(i) Probability that match would end in 2 sets.
If Roger wins: 0.6*0.7=0.42
If Andy wins: 0.4*0.75=0.3
Add them.

(ii) If match ends in 2 sets find the probability that match Andy won the match
0.3/0.72
Ans: (i) 0.72 (ii) 0.417

Q4 (i) [3 marks] (ii) [4 marks] (iii) [2 marks]
Coin A is thrown twice and Coin B once
Coin A has probability of head= 2/3
Coin B has probability of head= 1/4

(i) Show that the probability of getting 1 head is 13/36
If Coin A gives 1 head and Coin B gives none: 2*2/3*1/3*3/4=12/36 (Multiplied by 2 as both throws on Coin A can give a head)
If Coin A gives 0 heads and Coin B gives 1 head: 1/3*1/3*1/4=1/36
Add them and total= 13/36

(ii) Draw a probability distribution table of numbers of heads obtained
0 when no heads obtained: 1/3*1/3*3/4=3/36
2 when Coin A gives 2 heads: 2/3*2/3*3/4=12/36
Both Coin A and Coin B give one head each: 2*1/3*2/3*1/4=4/36 (Multiplied by 2 as both throws on Coin A can give a head)
Add them.
3 when all heads: 2/3*2/3:1/4=4/36

(iii) Find the expected value
1*13/36 + 2*16/36 +3*4/36=19/12
Ans : (ii) 0: 3/36 1:13/36 2: 16/36 3:4/36 (iii) 1.58

Q5 (i) [2 marks] (ii) [3 marks] (iii) [3 marks]
1345789 is a number

(i) Find the number of arrangements when odd numbers together and digits not repeated
5!*3! =720

(ii) Arrangements between 3000 and 5000 and even numbers and digits not repeated
When starting with 3: Last digit can be 4 or 8 so the middle two digits are 5P2=5P2*2!=40
When starting with 4: Last digit is 4 so middle two digits are 5P2=20
Total arrangements = 60

(iii) Multiples of 5 less than 1000 and digits ARE REPEATED
Last digit has to be 5 and can be 3-digit, 2-digit or 1-digit number
When 3 digit number: 7*7*1=49
When 2 digit number: 7*1=7
When 1-digit number: 1
Total =57
Ans: (i) 720 (ii) 60 (iii) 57

Q6 (i) [1 mark] (ii) [4 marks] (iii) [4 marks]
Total athletes=57
<10 were 0 <10.5 were 4 <11.0 were 10 <12.0 were 40 <12.5 were 49 <13.5 were 57

(i) Find in the interval 10.5-11.0 =6

(ii) Draw a histogram
Frequencies: 4,6,30,9,8
Frequency densities: 8,12,30,18,8

(iii) Calculate mean and variance
Mid-points: 10.2, 10.7, 11.45, 12.2, 12.95
Mean=11.6
Variance=0.547
Ans: (i) 6 (iii) 11.6, 0.547
Q7 (i) [3 marks] (ii) [2 marks] (iii) [6 marks]
Rafa studies at mean rate 1.9. The probability of studying more than 1.35 is 0.8

(i) Find Standard Deviation
Z=0.842 so S.D. =0.653
(ii) Find the probability that studies less than 2.0
(2.0-1.9)/0.653=0.1531
P=0.561

(iii) 200 samples are taken. Find the probability between 163 and 173 inclusive
np=160 npq=32
Less than 173.5: 0.9915
Less than 162.5: 0.6707
Between them= 0.321
Ans: (i) 0.653 (ii) 0.561 (iii) 0.321

Feel free to post any queries or mistakes :)
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All same Alhamdulillah :)
 
R

randomcod

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unkidd said:
p1 65 p3 55 p4 35 p6 45 i think this will be the gt
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Nope. Absolutely not. P1 was much harder than other years. 58 or 59. P6 was moderate but tricky, with too many places in which people could make dumb, careless mistakes. 45 is way over expected GT. 40 at the very very most. Dunno about the rest, haven't done them.
 
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