4 a certain type of tomato seed germinates 90 of the time...

4. A certain type of tomato seed germinates 90% of the time. Suppose a farmer plants 200 of these seeds. a) What's the probability exactly 90% of them germinate? b) What's the probability fewer than 175 germinate?

Transcript

00:02 Hello, this question is related to the binomial distribution.

00:06 Okay, so here we are given that the probability of success of germinating a seed is 0 .9 and sorry, this is p.

00:16 Okay, and q would be 1 minus p.

00:19 It means probability of failure that would be 0 .1.

00:21 And, and here is 25, that 25 sheets are taken at random.

00:28 Okay, so we need to calculate.

00:30 What is the probability that exactly 20 of them would germinate? okay.

00:35 So for probability, for 20 of them would germinate, it would be n, cr, n is 25, cr is 20 into 0 .9 to the power 20 into 0 .1 to the power 5.

00:51 Or n minus r, that would be 5.

00:54 So 25, sorry, 25 c20 into 0 .9 to the power 20 into 0 .1 to the power 5.

01:07 So exactly 20 seeds would germinate, it has a probability of 0 .0 .6 .6.

01:15 This is the probability.

01:16 Okay.

01:17 So in b part, what does it says? it says that what is the probability that 20 or more will germinate.

01:24 So priority of 20 we have already calculated, you will calculate probability of 21, 22, 23, 24 and similarly 20.

01:36 This was 24, 25.

01:39 Okay.

01:41 So i will write formula for 1, then rest of all, i will just directly write the answers.

01:47 So 21, 25, c21, 0 .9 to the power 21 into 0 .1 to the power 1 .1 to the power.

01:55 4 so this would be 25 c 21 into 019 to the power 21 into 0 .1 to the power 4 so it is coming out to be 0 .138 4 so next would be 25 c 22 into 0 .9 to the power 22 into 0 .1 to the power 3 so this would be 0 .2 to 625 again, 25c23 into 0 .9 to the power 23 into 0 .1 to the power.

02:39 So it is coming out to be 0 .2659...

Question

4. A certain type of tomato seed germinates 90% of the time. Suppose a farmer plants 200 of these seeds. a) What's the probability exactly 90% of them germinate? b) What's the probability fewer than 175 germinate?

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