Answer :
Final answer:
The answer involves using normal approximation to find probabilities. This involves standardization and using Z tables to find probabilities for coin toss results and a scenario of a ship carrying polar bears.
Explanation:
The question concerns two cases of the normal approximation to a probability distribution. In the first, we need to approximate the probability of getting between 196 and 205 heads in 400 tosses of a fair coin. In the second case, we need to approximate the probability that an arctic ship with a maximum weight capacity of 330,000 pounds can carry 400 polar bears with a mean weight of 800 pounds and a standard deviation of 100 pounds.
First Case:
For the first case, we take the expected number of heads (mean) as 200 (0.5 * 400), with the standard deviation sqrt(400 * 0.5 * 0.5) = 10. The number of heads is then standardised and looked up in the Z table for the values of 196 - 200 and 205 - 200.
Second Case:
The second case is a similar procedure with a weight problem. We calculate the mean total weight of 400 bears is 320,000 lbs, with a standard deviation of 2,000 lbs. Then we seek the Z-score for 330,000 - 320,000 lbs and look up this value in the standard normal cdf.
Learn more about Normal Approximation here:
https://brainly.com/question/35702705
#SPJ11