Question

7. A researcher found that there is an increase in undergraduate students doing part- time jobs to partially support their expenses. It is assumed that 55% of UWindsor students do part time jobs in this current year. The researcher randomly selected 150 UWindsor students and checked whether they work part-time jobs. Answer the following based on this data:

   1. Find the probability that more than 90 students of these 150 selected said that they do part-time jobs.

   2. Find the probability that less than 80 students of these 150 selected said that they do part-time jobs.

Answer 1

1) probability that more than 90 students of these 150 selected said that they do part-time jobs = 0.1092

2) probability that less than 80 students of these 150 selected said that they do part-time jobs=0.3405

Working:

We have given below information

P0=0.55 =% of UWindsor students do part time jobs in this current year.

n=150

1)

Find the probability that more than 90 students of these 150 selected said that they do part-time jobs.

We have to find p(P>90/150)=p(P>0.6)

We know that

z=(P-P0)/sqrt(P0*(1-P0)/n) ~ N(0,1)

p(P>0.6) = p(z>(0.6-0.55)/sqrt(0.55*(1-0.55)/150))

p(Z>1.2309)

=0.1092

2)

Find the probability that less than 80 students of these 150 selected said that they do part-time jobs

We have to find p(P<80/150)

=p(P<0.5333)

= p(z<(0.5333-0.55)/sqrt(0.55*(1-0.55)/150))

=p(Z<-0.4111)

=0.3405

Answer

1) probability that more than 90 students of these 150 selected said that they do part-time jobs = 0.1092

2) probability that less than 80 students of these 150 selected said that they do part-time jobs=0.3405