BIOSTATISTICS!! Please indicate the formulas used BIOSTATISTICS!! Please indicat

Question

BIOSTATISTICS!! Please indicate the formulas used BIOSTATISTICS!! Please indicate the formulas used 3) A rare physically incapacitating condition in children occurs with a probability of p 5. Imagine that you can detect this defect immediately after birth which can help mitigate the condition through physical therapy. You determine the presence or absence of the condition at birth through a blood test and you sample 50,000 newborns over a year. a) What is the expected number that will have the birth defect? b) What is the probability that 0 have the defect? c) What is the probability that there is at least 1 child with the defect? d) What is the probability that there are no more than 2 children with the defect?

Explanation / Answer

Binomial distribution used.

n=50000

p=0.00005

a). expected number = n*p=50000*0.00005=2.5

b).

P(X=x) = (nCx) px (1-p)n-x   

P(X=0) = (50000C0) 0.000050 (1-0.00005)50000-0   

P(X = 0) = 0.0821

c) P( at least 1 defect) = 1-P( x=0)

=1-0.0821 =0.9179

d).

P( no more than 2 defect)= P( 2 defects)

=P(x=0)+P( x=1)+P(X=2)

=0.0821+ 0.2052+ 0.2565

=0.5438

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