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Chapter 6: Q. 79 (page 404)

79. Sowing seeds Refer to Exercise 69.

(a) Find the probability that exactly17 seeds germinate. Show your work.
(b) If only 12seeds actually germinate, should Judy be suspicious that the company鈥檚 claim is not true? Compute P(X鈮�12)and use this result to support your answer.

Short Answer

Expert verified

(a) The probability that exactly 17seeds germinate is P(X=17)=24.28%.

(b) Judy should be suspicious and the value isP(X鈮�12)鈮�0.0059鈮�0.59%.

Step by step solution

01

Part (a) Step 1: Given information 

The probability for the exactly 17seeds germinate.

02

Part (a) Step 2: Explanation 

Given: n=20, and p=0.85
The Binomial Probability:
P(X=k)=nk脳pk脳(1鈭�p)n鈭�k

P(X=17)=2017脳(0.85)17脳(0.15)20鈭�17鈮�0.2428=24.28%

03

Part (b) Step 1: Given information 

Let,12 seeds actually germinate. And compute the value P(X鈮�12).

04

Part (b) Step 2: Explanation 

Given: n=20, and p=0.85.

Let's use the binomial Probability:

P(X=k)=nk脳pk脳(1-p)n-k
P(X鈮�12)=P(X=0)+P(X=1)+鈥�+P(X=12)鈮�0.0059鈮�0.59%

As a result, the probability is low (less than0.05), indicating that the event is unlikely to happen by chance.

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