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%=10080​=54​=0.8 r=1−q=1−0.8=51​=0.2 n=10  n1​=(1n​)⋅q1⋅(1−q)n−1=(110​)⋅0.81⋅(1−0.8)10−1=10⋅0.81⋅0.29≐4.096⋅10−6 n2​=(2n​)⋅q2⋅(1−q)n−2=(210​)⋅0.82⋅(1−0.8)10−2=45⋅0.82⋅0.28≐0.0001 n3​=(3n​)⋅q3⋅(1−q)n−3=(310​)⋅0.83⋅(1−0.8)10−3=120⋅0.83⋅0.27≐0.0008 n4​=(4n​)⋅q4⋅(1−q)n−4=(410​)⋅0.84⋅(1−0.8)10−4=210⋅0.84⋅0.26≐0.0055 n5​=(5n​)⋅q5⋅(1−q)n−5=(510​)⋅0.85⋅(1−0.8)10−5=252⋅0.85⋅0.25≐0.0264 n6​=(6n​)⋅q6⋅(1−q)n−6=(610​)⋅0.86⋅(1−0.8)10−6=210⋅0.86⋅0.24≐0.0881 n7​=(7n​)⋅q7⋅(1−q)n−7=(710​)⋅0.87⋅(1−0.8)10−7=120⋅0.87⋅0.23≐0.2013 n8​=(8n​)⋅q8⋅(1−q)n−8=(810​)⋅0.88⋅(1−0.8)10−8=45⋅0.88⋅0.22≐0.302 n9​=(9n​)⋅q9⋅(1−q)n−9=(910​)⋅0.89⋅(1−0.8)10−9=10⋅0.89⋅0.21≐0.2684 n10​=(10n​)⋅q10⋅(1−q)n−10=(1010​)⋅0.810⋅(1−0.8)10−10=1⋅0.810⋅0.20≐0.1074  n8​ > ∀ni​  m=8

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