Chpt 6 | ||||||
A study by Stanford University concluded that 45% of college | ||||||
students sleep at least 8 hours per night. In a sample | ||||||
of 10 DCCC students, find the probability that | ||||||
at least 8 of the 10 get 8 or more. | ||||||
Solution:
Here, we have to use binomial distribution formula for finding the required probability.
We are given
p = 0.45,
q = 1 – p = 1 – 0.45 = 0.55
n = 10,
We have to find P(X≥8)
P(X≥8) = P(X=8) + P(X=9) + P(X=10)
P(X=x) = nCx*p^x*q^(n – x)
P(X=8) = 10C8*0.45^8*0.55^(10 – 8)
P(X=8) = 45*0.45^8*0.55^2
P(X=8) = 0.02289
P(X=9) = 10C9*0.45^9*0.55^(10 – 9)
P(X=9) = 10*0.45^9*0.55^1
P(X=9) = 0.004162
P(X=10) = 10C10*0.45^10*0.55^(10 – 10)
P(X=10) = 1*0.45^10*0.55^0
P(X=10) = 0.000341
P(X≥8) = P(X=8) + P(X=9) + P(X=10)
P(X≥8) = 0.02289 + 0.004162 + 0.000341
P(X≥8) = 0.027393
Required probability = 0.027393
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