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Slav-nsk [51]
3 years ago
11

The average weight of a newborn panda is 0.2, or 2/10 pound. Between what two integers is the weight of a newborn panda?​

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
6 0

Answer:

\frac{2}{10} lies between 0 and 1.

Step-by-step explanation:

We must have in mind that given average weight of a newborn panda is a non-integer rational number, such that lies between two integer rational number. In other words, this number must satisfy the following condition:

n < \frac{a}{b} < n +1, n, a, b \in \mathbb{N}_{O}

\mathbb{N}_{O} = \mathbb{N}\,\cup\,{\{0\}}

Which is now developed mathematically to deduce a useful expression to find integers:

1) n < \frac{a}{b} < n +1 Given

2) n \cdot 1 < \frac{a}{b} < n\cdot 1 + 1 Modulative property

3) n \cdot (b\cdot b^{-1}) < a\cdot b^{-1} < n \cdot (b\cdot b^{-1}) + b\cdot b^{-1} Existence of Multiplicative inverse/Definition of division.

4) (n\cdot b)\cdot b^{-1} < a\cdot b^{-1}< [(n+1)\cdot b] \cdot b^{-1} Commutative, Associative and Distributive properties.

5) n\cdot b < a < (n+1)\cdot b Compatibility with Multiplication/Existence of Multiplicative Inverse/Modulative Property/Result.

If we know that a = 2 and b = 10, the following inequation is formed:

10\cdot n < 2 < 10\cdot (n+1)

It is quite evident to conclude that \frac{2}{10} lies between 0 and 1.

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Answer:

The required probability is 0.94

Step-by-step explanation:

Consider the provided information.

There are 400 refrigerators, of which 40 have defective compressors.

Therefore N = 400 and X = 40

The probability of defective compressors is:

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It is given that If X is the number among 15 randomly selected refrigerators that have defective compressors,

That means n=15

Apply the probability density function.

P(X=x)=^nC_xp^x(1-p)^{n-x}

We need to find P(X ≤ 3)

P(X\leq3) =P(X=0)+P(X=1)+P(X=2)+P(X=3)\\P(X\leq3) =\frac{15!}{15!}(0.1)^0(1-0.1)^{15}+\frac{15!}{14!}(0.1)^1(1-0.1)^{14}+\frac{15!}{13!2!}(0.1)^2(1-0.1)^{13}+\frac{15!}{12!3!}(0.1)^3(1-0.1)^{12}\\

P(X\leq3) =0.944444369992\approx 0.94

Hence, the required probability is 0.94

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