Final answer:
To find the probability of obtaining between 270 and 302 heads inclusive when a coin is tossed 576 times, use the normal curve approximation.
Step-by-step explanation:
To find the probability of obtaining between 270 and 302 heads inclusive when a coin is tossed 576 times, we can use the normal curve approximation. The first step is to calculate the mean and standard deviation. The mean (µ) is equal to n * p, where n is the number of trials and p is the probability of success for each trial. In this case, n = 576 and p = 0.5 since the coin has a 50% chance of landing on heads or tails.
The standard deviation (σ) is calculated using the formula √(n * p * (1 - p)). Substitute the values n = 576 and p = 0.5 into the formula to find the value of σ.
Next, we standardize the range of 270 to 302 by subtracting the mean (270 - µ) and dividing by the standard deviation (σ). Call this value A. Repeat the process for the upper limit of the range (302 - µ) divided by σ to get value B.
Finally, we use a standard normal distribution table or a calculator to find the probability between A and B, which corresponds to the probability of obtaining between 270 and 302 heads inclusive. This probability can be interpreted as the area under the normal curve between A and B.