A set of five similar coins is tossed 320 times and the result is
No of heads 0 1 2 3 4 5
Frequency 6 27 72 112 71 32
Test the hypothesis that the data follow a binomial distribution:
(
2 = 11.07 5 . )
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The foundation of physics rests upon physical quantities in term of which the laws of physics are expressed. Therefore, these quantities have to be measured accurately. Physical quantities are often divided into two categories; base quantities and derived quantities. Derived quantities are those quantities which are derived from other physical quantities. Examples of derived quantities are force, velocity, acceleration etc.
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Step-by-step explanation:
Given A set of five similar coins is tossed 320 times and the result is No of heads 0 1 2 3 4 5
Frequency 6 27 72 112 71 32
Test the hypothesis that the data follow a binomial distribution:
- So the probability of a head or a tail will be ½ . Therefore the frequency will be the next term of binomial expansion.
- So we get, since 5 similar coins,
- 320 (1/2 + ½)^5
- Now we need to expand, so we get
- 320 [ (1/2)^5 + 5(1/2)^4 (1/2) + 10 (1/2)^3(1/2)^2 + 10(1/2)^2(1/2)^3 + 5(1/2)(1/2)^4 + (1/2)^5]
- 320 [ 1/32 + 5 (1/32) + 10 (1/32) + 10 (1/32) + 5(1/32) + 1/32]
- 320 /32 ( 1 + 5 + 10 + 10 + 5 + 1)
- 10 ( 1 + 5 + 10 + 10 + 5 + 1)
- 10 + 50 + 100 + 100 + 50 + 10
- Now the frequencies are 10,50,100,100,50,10
- Therefore
- So let m be the heads
- So m^2 = (6 – 10)^2 / 10 + (27 – 50)^2 / 50 + (72 – 100)^2 / 100 + (112 – 100)^2 / 100 + (71 – 50)^2 / 50 + (32 – 10)^2 / 100
- = 16 / 10 + 529 / 50 + 784 /100 + 144 / 100 + 441 / 50 + 484 / 100
- = 160 + 1058 + 784 + 144 + 882 + 484 / 100
- = 3512 / 100
- = 35.12
- So number of degrees of freedom will be number of data set – 1
- So 6 – 1
- = 5
- Now the value for 5 will be 11.07. Now the obtained value is greater than this value.
- Therefore the data does not follow binomial theorem.
Reference link will be
https://brainly.in/question/30858590
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