Question

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7) (10 point) (Binomial) According to the 2018 Utah Dept of Health immunization report, approximately 5% of kindergarten students statewide have claimed immunization exemption. In a class of 20 students, what is the likelihood that no child has received an exemption? What is the likelihood that at least one child has received an exemption?

Answer 1

probability of clamming immunization exemption by a student= 0.05

now, let x= number of students having exemption   $p(x)=0.05*e^{-x}$ ; x=0,1,2,....20

likelihood function

$L= \prod_{x=0}^{20}p(x)\\ L=(0.05)^{20}*e^{\sum_{x=0}^{20}x}\\ L=(0.05)^{20}*e^{\sum_{x=0}^{20}x}\\$

Likehood that no child has received an exemption

Likehood that atleast one child has received an exemption

$=(0.05)^{20}(1+e)$