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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, 2140 germinated. (a) Use relative frequencies to estimate the probability that a seed will germinate. What is your estimate? (Enter your answer to 3 decimal places.)

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Answer:

The probability that a seed will germinate is 0.713.

Step-by-step explanation:

The probability of an event is a theoretical idea that is useful when there are several equally likely outcomes.

The relative frequency of an event is a practical idea: it describes what fraction of the time an event occurred.

In the long run, the relative frequency of an event will be close to the (theoretical) probability.

A probability assignment based on relative frequency uses the formula

[tex]\:Probability \:of \:event= \:relative \:frequency = \frac{f}{n}[/tex]

where [tex]f[/tex] is the frequency of the event occurrence in a sample of [tex]n[/tex] observations.

We know:

  • The sample n = 3000 seeds.
  • The frequency of the event  f = 2140 germinated.

The probability is the number of favorable outcomes divided by the number of possible outcomes:

Let G the event "The seed germinated"

[tex]P(G)=\frac{f}{n}=\frac{\# \:of \:favorable \:outcomes}{\# \:of \:possible \:outcomes} \\\\P(G)=\frac{2140}{3000} =0.713[/tex]

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