23.A botanist has developed a new hybrid cotton plant that can withstand insects

Question

23.A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant. To estimate the probability that a seed from the new plant will germinate, a random sample of 3000 seeds was planted in warm, moist soil. Of these seeds, 2210germinated.

(a) Use relative frequencies to estimate the probability that a seed will germinate. What is your estimate? (Enter your answer to 3 decimal places.)


(b) Use relative frequencies to estimate the probability that a seed will not germinate. What is your estimate? (Enter your answer to 3 decimal places.)


(c) Either a seed germinates or it does not. What is the sample space in this problem?

germinategerminate or not germinate    not germinate

Do the probabilities assigned to the sample space add up to 1? Should they add up to 1? Explain.

Yes, because they cover the entire sample space.Yes, because they do not cover the entire sample space.    No, because they cover the entire sample space.No, because they do not cover the entire sample space.

(d) Are the outcomes in the sample space of part (c) equally likely?

yesno   

Explanation / Answer

a.
seed from the new plant will germinate (x)=2210
Sample Size(n)=3000
probability that a seed will germinate Sample proportion = x/n =0.737

b.
probability that a seed will not germinate = 1 - (x/n) = 1 - 0.737 = 0.263

c. the sample space = 3000
Yes, because they cover the entire sample space

d.
no

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