2x - 3y = 8 -2x + 6y = -20 x = ? y = ? solve the system of equations
1 answer:
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Answer:
(1) A Normal approximation to binomial can be applied for population 1, if <em>n</em> = 100.
(2) A Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50 and 40.
(3) A Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50, 40 and 20.
Step-by-step explanation:
Consider a random variable <em>X</em> following a Binomial distribution with parameters <em>n </em>and <em>p</em>.
If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
The three populations has the following proportions:
p₁ = 0.10
p₂ = 0.30
p₃ = 0.50
(1)
Check the Normal approximation conditions for population 1, for all the provided <em>n</em> as follows:
Thus, a Normal approximation to binomial can be applied for population 1, if <em>n</em> = 100.
(2)
Check the Normal approximation conditions for population 2, for all the provided <em>n</em> as follows:
Thus, a Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50 and 40.
(3)
Check the Normal approximation conditions for population 3, for all the provided <em>n</em> as follows:
Thus, a Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50, 40 and 20.
Answer :
Let's assume the opposite of the statement i.e., 3 + √5 is a rational number.
Since, a, b and 3 are integers. So,
Here, it contradicts that √5 is an irrational number.
because of the wrong assumption that 3 + √5 is a rational number.
Hence, 3 + √5 is an irrational number.