Question

1. Student grant application forms are not always completed correctly. Studies in a particular o¢ ce show that during a two month period 9% of forms had to be returned to the applicants for correct completion. Fifty application forms are selected at random to determine the number of applications that needed to be returned.

(a) State the random variable. [1 mark]

(b) Using the statistical tables, Önd the probability that:

i. More than ten applications have to be returned;

ii. Less than Öve applications have to be returned;

iii. Between eight and twelve (inclusive) applications have to be returned. [3 marks each]

Answer 1

Ans:

a)We can use binomial random variable.

x=number of applications that needed to be returned out of 50

n=50,p=0.09

b)

P(x=r)=50C_r*0.09^r*(1-0.09)^50-r

i)P(x>10)=1-P(x<=10)=1-binomdist(10,50,0.09,true)=0.0043

ii)P(x<1)=P(x=0)=(1-0.09)^50=0.0090

iii)P(8<=x<=12)=P(x<=12)-P(x<=7)

=binomdist(12,50,0.09,true)-binomdist(7,50,0.09,true)

=0.9996-0.9231

=0.0765