Respuesta :
Answer:
A
Step-by-step explanation:
This is a Bernoulli trial problem.
Since the probability that the seed will germinate is 80% or 0.8, the probability that they won’t germinate is 0.2
Now let’s say the probability to germinate is p and the probability not to is a, we can now set up the Bernoulli equation in this regard. Since we are proposing that exactly 14 will germinate, it means 6 are not expected to germinate
P(14) = 20C14 (0.8)^14 (0.2)^6 = 0.109099700973
Option A is the right answer
You can use binomial distribution here.
The probability that exactly 14 seeds will germinate is given by:
Option A: 0.1091 is correct
Given that:
- Company claims that 80% of lima bean seeds will germinate.
- Callie buys 20 lima beans
To find:
Probability that exactly 14 seeds will germinate.
Using binomial distribution to get the needed probability:
We use binomial distribution when we have to track success and failure of multiple objects(multiple Bernoulli trials)
Let X be the random variable tracking the number of seeds that will germinate out of 20 seeds. The success probability is 80% or 0.8(showing probability of germination)
Thus. [tex]X \sim B(20, 0.8)[/tex]
The probability of X = x is given by:
[tex]P(X = x) = \: ^{20}C_x (0.8)^x (1-0.8)^{20-x}[/tex]
Thus:
[tex]P(X = 14) = \: ^{20}C_{14} (0.8)^{14} (1-0.8)^{20-14} = 38760 \times 0.04398 \times 0.000064 = 0.109\\P(X = 14) = 0.10909.. \approx 0.1091[/tex]
The probability that exactly 14 seeds will germinate is given by:
Option A: 0.1091 is correct
Learn more about binomial distribution here:
https://brainly.com/question/8152053
