Final answer:
To find the probability of a sample containing 52% or more overweight or obese children, calculate the z-score and use technology such as a graphing calculator or software to find the cumulative probability. A calculator function like normalcdf can determine the area to the right of the z-score, or invNorm for the left cumulative probability.
Step-by-step explanation:
To calculate the probability that the random sample of 200 children will contain 52% or more who are overweight or obese using the model N(0.55, 0.035), you would first need to determine the z-score corresponding to 52%. The z-score formula is (x - μ) / σ, where x represents the value you're testing (0.52), μ is the mean (0.55), and σ is the standard deviation (0.035).
After calculating the z-score, you can use technology like a graphing calculator or statistical software to find the probability. For example, on a TI-83/84 calculator, you would use the normalcdf function with the z-score as the lower bound and a very high number (like 9999) as the upper bound to represent the right tail of the curve. Alternatively, using the invNorm function would provide the z-score for a given cumulative probability to the left. The area to the right, which you are interested in, is 1 minus this cumulative probability.