The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial.The binomial distribution is used to obtain the probability of observing x successes in n trials, with the probability of success on a single trial denoted by p. The binomial distribution assumes that p is fixed for all trials. The formula for the binomial probability mass function is
P(X=x)=(nx)px(1−p)n−x 3.1.1 Exactly 4 will have a medical aid.
P(X=4)=(104)0.34(1−0.3)10−3=0.200120949 3.1.2 At least 2 will have a medical aid.
P(X≥2)=1−P(X<2)=1−P(X=0)−P(X=1)=
=1−(100)0.30(1−0.3)10−0−(101)0.310(1−0.3)10−10=0.850692 3.1.3 More than 9 will have a medical aid.
P(X>9)=P(X=10)=(1010)0.310(1−0.3)10−10=0.000006 3.2
μ=45,σ=8
z=σx−μ
z1=845−45=0,z2=851−45=0.75
P(45<X<51)=P(0<Z<0.75)=0.273373
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