A lvl H2 Maths: Binomial Distribution

Question from http://www.sgforums.com/forums/2297/topics/355089

A dancer performs a certain routine faultlessly 80% of the time. Using a suitable approximation, find the probability that in 160 such occasions, she will perform the routine faultlessly on at least 75% of the number of such occasions.

*************************

Answer:


Y ~ B(160, 0.8)
Let X be the Normal Approximation to Binomial, i.e. X ~ N (128, 25.6)

75% of 160 = 120

Thus,
P(Y > 120) = P(X ≥ 120.5) by Normal Approximation
= 0.931 using Graphic Calculator

A lvl H2 Maths: Binomial Distribution

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