Question

Here is a question where you can see the usefulness of looking at a sample size greater than 1 . When people get on a roller coaster, it is usually more than one person: *The maximum safe total weight for riding a particular roller coaster is 12,000lbs. The roller coaster seats 60 people. If 60 males are riding the roller coaster, what is the probability that their mean weight exceeds 200lbs ? Note: 200×60=12,000 (the maximum weight capacity) Assume the mean weight of men, in general, is 194lbs and a standard deviation 68lbs. Sketch the graph and show what you entered into the calculator.

Answer 1

To find the probability that the mean weight of 60 males riding a roller coaster exceeds 200 pounds, use the Central Limit Theorem and the z-score formula.

Step-by-step explanation:

To find the probability that the mean weight of 60 males riding a roller coaster exceeds 200 pounds, we can use the Central Limit Theorem. According to the theorem, for a large sample size, the distribution of sample means will be approximately normal, regardless of the shape of the original population distribution.

In this case, the sample mean follows a normal distribution with a mean equal to the population mean, which is 194 pounds, and a standard deviation equal to the population standard deviation divided by the square root of the sample size, which is 68 pounds divided by the square root of 60.

To find the probability that the mean weight exceeds 200 pounds, we can standardize the distribution using the z-score formula: z = (x - mean) / standard deviation. Substituting the values, we get: z = (200 - 194) / (68 / sqrt(60)). Calculating this value, we can then use the Z-table or a calculator to find the probability associated with this z-score.