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daosau377
06.06.2020 •
Mathematics
In a study, 37% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to nuclear plant. Among 12 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health.
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Ответ:
The probability that when 12 adults are randomly selected, 3 or fewer are in excellent health is 0.2946
Step-by-step explanation:
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 12 * 0.37
= 4.44
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 12 * 0.37 * 0.63
= 2.7972
III.
standard deviation = sqrt( variance ) = sqrt(2.7972)
=1.6725
the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health
P( X < = 3) = P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 12 3 ) * 0.37^3 * ( 1- 0.37 ) ^9 + ( 12 2 ) * 0.37^2 * ( 1- 0.37 ) ^10 + ( 12 1 ) * 0.37^1 * ( 1- 0.37 ) ^11 + ( 12 0 ) * 0.37^0 * ( 1- 0.37 ) ^12
= 0.2947
Ответ:
An octagon has 8 sides of equal length.
P = 8s = 8 * 8 cm = 64 cm
64 cm