Question

Heights of 10 year old children, regardless of sex, closely follow a normal distribution with mean 54.1 inches and standard deviation 6.6 inches. Round answers to 4 decimal places. a) What is the probability that a randomly chosen 10 year old child is less than 49.2 inches?

Answer 1

The probability that a randomly chosen 10-year-old child is less than 49.2 inches is approximately 0.2296 or 22.96%.

Step-by-step explanation:

To find the probability that a randomly chosen 10-year-old child is less than 49.2 inches, we need to standardize the value 49.2 using the given mean and standard deviation. The standardized value (z-score) is calculated using the formula: z = (x - mean) / standard deviation.

So, in this case: z = (49.2 - 54.1) / 6.6 = -0.7424.

Next, we need to find the cumulative probability corresponding to this z-score. By referring to a standard normal distribution table or using a calculator, we can find that the cumulative probability for a z-score of -0.7424 is approximately 0.2296. Therefore, the probability that a randomly chosen 10-year-old child is less than 49.2 inches is 0.2296 or 22.96%.