Question

Suppose at random 39% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=37. What is the probability that 8 or more children become sick?

Answer 1

Given :

Probability of success = p = 0.39

Number of sample = n = 37

Let X be the number of children become sick.

X ~ Binomial (n=37, p=0.39)

The probability density function of Binomial distribution is given by

P(X=X) = (nCx) * p^x * (1-p)^x

The probability that 8 or more children become sick :

P(X8) = 1 - P(X<8)

= 1 - (37Cx) * (0.39)^x * (1-0.39)^37-x

= 1 - 0.0076

= 0.9924

P(X8) = 0.9924

Therefore the probability that 8 or more children become sick is 0.9924