Discussion [Maths]

[Daniel Koh]

Hey everyone,

Here's the discussion questions for Maths. Only two. :)

Q1. A telephone enquiry service is so busy that only 80% of calls to
it are successfully connected. It may be assumed that all calls are
independent. Twelve calls are made at random to the service. Find the
probability that at least 9 are successfully connected.

After improving the facilities, the management arranges for a random
sample of 120 calls to be made to the service and it is found that 105
of these calls are successfully connected. Test, at the 4%
significance level, whether the successful connection rate has
improved.

A consumer association carries out its own test using a random sample
of 150 calls and finds that the number of unsuccessful calls is 25.
Using this sample, find an approximate 92% confidence interval for the
proportion of calls that are unsuccessful.

Q2. A manufacturer of rockets estimates that, on average, 1 in 75 of
the rockets fail to burn properly. Using this estimate, and a Poisson
distribution, find an approximate value for the probability that, out
of 225 randomly chosen rockets, at most 221 burn properly.

[ for this question, i made alot of mistakes. First I went to normal,
and realized that my answer is wrong. Rather confusing.. but it's a
good question to build our concepts]

Daniel