Question from http://www.sgforums.com/forums/2297/topics/355089
It is claimed that 90% of the children who were given flu jabs do not catch flu in the next 6 months. A paediatrician gave a flu jab to 150 children in October. Find the least integer r such that the probability of less than r children catching flu within the next 6 months is more than 3%.
*************************
Answer:
Let X be the number of children catching flu within the next 6 months.
Hence,
X ~ B(150, 0.1)
P(X < r) = P(X ≤ r - 1)
We can use the graphic calculator to find the answer.
L1: 1 to 10
L2: binomcdf(150, 0.1, L1)
We see that when L1 is 8, L2 is 0.03074 (first number of L1 for L2 to be greater than 3%)
Therefore r -1 = 8,
r= 9
Least integer r = 9
