Final answer:
To find the probability of getting between 730 and 770 heads (inclusive) when flipping a coin with a probability of heads of 0.38, we can use the normal approximation to the binomial distribution. The probability is approximately 0.588.
Step-by-step explanation:
To find the probability of getting between 730 and 770 heads (inclusive) when flipping a coin with a probability of heads of 0.38, we can use the normal approximation to the binomial distribution.
The mean of the binomial distribution is given by n * p, where n is the number of trials (2000) and p is the probability of success (0.38). So the mean is 2000 * 0.38 = 760.
The standard deviation of the binomial distribution is given by sqrt(n * p * (1 - p)), where sqrt() represents the square root. So the standard deviation is sqrt(2000 * 0.38 * (1 - 0.38)) = sqrt(483.2) = 21.98 (rounded to two decimal places).
Now, we can use the normal distribution to find the probability of getting between 730 and 770 heads. We standardize the intervals by subtracting the mean and dividing by the standard deviation. For 730 heads: (730 - 760) / 21.98 ≈ -1.36, and for 770 heads: (770 - 760) / 21.98 ≈ 0.45.
Next, we use a standard normal distribution table or calculator to find the respective probabilities of these z-scores. The probability of getting a z-score less than -1.36 is approximately 0.085 and the probability of getting a z-score less than 0.45 is approximately 0.673. To find the probability between these two z-scores, we subtract the smaller probability from the larger probability: 0.673 - 0.085 = 0.588.
Therefore, the probability of getting between 730 and 770 heads (inclusive) is approximately 0.588.