Seeds

We randomly selected ten seeds from a box of spruce seeds with an 80% germination rate and planted them. Find the median of the random variable, the number of germinating seeds.

Correct answer:

m = 8

Step-by-step explanation:

q = 80 % = \frac{8 0}{1 0 0} = \frac{4}{5} = 0.8 r = 1 - q = 1 - 0.8 = \frac{1}{5} = 0.2 n = 10 n_{1} = (1 n) \cdot q^{1} \cdot (1 - q)^{n - 1} = (1 1 0) \cdot 0 . 8^{1} \cdot (1 - 0.8)^{10 - 1} = 10 \cdot 0 . 8^{1} \cdot 0 . 2^{9} ≐ 4.096 \cdot 1 0^{- 6} n_{2} = (2 n) \cdot q^{2} \cdot (1 - q)^{n - 2} = (2 1 0) \cdot 0 . 8^{2} \cdot (1 - 0.8)^{10 - 2} = 45 \cdot 0 . 8^{2} \cdot 0 . 2^{8} ≐ 0.0001 n_{3} = (3 n) \cdot q^{3} \cdot (1 - q)^{n - 3} = (3 1 0) \cdot 0 . 8^{3} \cdot (1 - 0.8)^{10 - 3} = 120 \cdot 0 . 8^{3} \cdot 0 . 2^{7} ≐ 0.0008 n_{4} = (4 n) \cdot q^{4} \cdot (1 - q)^{n - 4} = (4 1 0) \cdot 0 . 8^{4} \cdot (1 - 0.8)^{10 - 4} = 210 \cdot 0 . 8^{4} \cdot 0 . 2^{6} ≐ 0.0055 n_{5} = (5 n) \cdot q^{5} \cdot (1 - q)^{n - 5} = (5 1 0) \cdot 0 . 8^{5} \cdot (1 - 0.8)^{10 - 5} = 252 \cdot 0 . 8^{5} \cdot 0 . 2^{5} ≐ 0.0264 n_{6} = (6 n) \cdot q^{6} \cdot (1 - q)^{n - 6} = (6 1 0) \cdot 0 . 8^{6} \cdot (1 - 0.8)^{10 - 6} = 210 \cdot 0 . 8^{6} \cdot 0 . 2^{4} ≐ 0.0881 n_{7} = (7 n) \cdot q^{7} \cdot (1 - q)^{n - 7} = (7 1 0) \cdot 0 . 8^{7} \cdot (1 - 0.8)^{10 - 7} = 120 \cdot 0 . 8^{7} \cdot 0 . 2^{3} ≐ 0.2013 n_{8} = (8 n) \cdot q^{8} \cdot (1 - q)^{n - 8} = (8 1 0) \cdot 0 . 8^{8} \cdot (1 - 0.8)^{10 - 8} = 45 \cdot 0 . 8^{8} \cdot 0 . 2^{2} ≐ 0.302 n_{9} = (9 n) \cdot q^{9} \cdot (1 - q)^{n - 9} = (9 1 0) \cdot 0 . 8^{9} \cdot (1 - 0.8)^{10 - 9} = 10 \cdot 0 . 8^{9} \cdot 0 . 2^{1} ≐ 0.2684 n_{10} = (1 0 n) \cdot q^{10} \cdot (1 - q)^{n - 10} = (1 0 1 0) \cdot 0 . 8^{10} \cdot (1 - 0.8)^{10 - 10} = 1 \cdot 0 . 8^{10} \cdot 0 . 2^{0} ≐ 0.1074 n_{8} > \forall n_{i} m = 8

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You need to know the following knowledge to solve this word math problem:

statistics

combinatorics

probability

arithmetic

comparing

basic operations and concepts

reason

Grade of the word problem

high school

Seeds

Correct answer:

Step-by-step explanation:

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