You sow 40 sunflower seeds, and 30 of them are germinated. Use experimental probability approximate the number of seeds that will germinate if you so 20
There are different methods to approach this problem, but one possible way is to use the experimental probability of germination to estimate the expected value or mean of a binomial distribution with n=20 and p=30/40.
The binomial distribution models the number of successes (germinated seeds) in a fixed number of independent trials (seeds sown) with a fixed probability of success in each trial. The mean of this distribution is given by the formula: E(X) = np, where X is the random variable representing the number of successes.
Using the experimental probability, we can estimate the value of p as the proportion of successful trials out of the total number of trials: p ≈ 30/40 = 0.75. Then, we can plug in n=20 and p=0.75 in the formula to get:
E(X) = np = 20 x 0.75 = 15
Therefore, we would expect about 15 seeds to germinate if we sow 20 sunflower seeds, assuming that the conditions are similar to those of the previous experiment. However, this estimate has some uncertainty and may vary from one trial to another, especially with a small sample size like 20. We could also use other measures of central tendency or dispersion to describe the possible outcomes, such as the median, mode, standard deviation, or range of the distribution.
To approximate the number of seeds that will germinate if you sow 20 seeds, we can use the experimental probability calculated from the previous scenario.
Experimental probability is computed by dividing the number of favorable outcomes (seeds germinated) by the total number of outcomes (seeds sown).
In the previous scenario:
Total seeds sown (N) = 40
Seeds germinated (F) = 30
Experimental probability (P) = F / N
P = 30 / 40
P = 0.75
Now, if we sow 20 seeds, we can estimate the number of seeds that will germinate by multiplying the experimental probability by the total number of seeds sown.
Number of seeds to be sown (n) = 20
Estimated number of seeds germinated (E) = P * n
E = 0.75 * 20
E = 15
Therefore, approximately 15 seeds will germinate if you sow 20 seeds, based on the experimental probability calculated in the previous scenario.