Question

It is known that 72.3% of statistics students do their homework in time for it to be collected and graded. Each student does homework independently. Students are selected randomly. In a statistics class of 44 students, a. what is the probability that at least 29 students will do their homework on time? Use the binmial probability formula. Round your answer to 3 decimals. b. what is the probability that exactly 31 will do their homework on time? Use the binomial probability formula. Round your answer to 3 decimals.

Answer 1

Question (a)

Given that 72.3% of statistics students do their homework ijn time for it to be collected and graded

So p = 0.723

q = 1 - p

= 1 - 0.723

= 0.277

Given n =44 and we want probability that at least 29 students will do their homework on time

that is case in binomial distribution with 29 or more cases till 44

the formala for binomail distribution of x successes exactly out of n trials

ncx * px * qn-x

where p is the porbability of success and q is the failure or 1-p

Here tjhe probability that at least 29 students will do their homework on time

=  44C29 * 0.72329 * 0.27744-29 + 44C30 * 0.72330 * 0.27744-30 + 44C31 * 0.72331 * 0.27744-31 + .......... till 44C44 * 0.72344 * 0.27744-44

= 0.081991 + 0.107003 + 0.126131 + 0.133744 + 0.12694 + 0.107194 + 0.07994 + 0.052163 + 0.029438 + 0.014154 + 0.005684 + 0.001854 + 0.000472 + 0.000088 + 0.0000107 + 0.0000006

= 0.866807466

= 0.867 rounde to three decimals

Question (b)

Probability that 31 students will exactly do homework on time = 44C31 * 0.72331 * 0.27744-31

= 0.126131

= 0.126