The probability that a seed will germinate is 0.34. Suppose 130 seeds are planted. How do you use the central limit theorem to determine the probability that at most 37 seeds germinate?

To use the central limit theorem to determine the probability that at most 37 seeds germinate out of 130 planted seeds, we first calculate the mean and standard deviation of the sample distribution.

Mean = n * p = 130 * 0.34 = 44.2 Standard deviation = sqrt(n * p * (1 - p)) = sqrt(130 * 0.34 * (1 - 0.34)) ≈ 5.16

Next, we standardize the value of 37 using the z-score formula:

z = (x - mean) / standard deviation = (37 - 44.2) / 5.16 ≈ -1.39

Now, we use a standard normal distribution table or a calculator to find the cumulative probability associated with this z-score.

Looking up the z-score of -1.39 in the standard normal distribution table, we find the cumulative probability to be approximately 0.0823.

Therefore, the probability that at most 37 seeds germinate out of 130 planted seeds is approximately 0.0823, or 8.23%.