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The weights of 1,000 children average 63 kg with a standard deviation of 17 kg. Suppose the weights are normally distributed. How many children weigh greater than 67 kg?

Answer :

Final answer:

To find the number of children weighing greater than 67kg, calculate the z-score for this weight using the formula z = (x - μ) / σ, then find the proportion in the standard normal distribution table to determine the number of children.

Explanation:

To find the number of children weighing greater than 67kg, we need to calculate the z-score for this weight using the formula z = (x - μ) / σ. In this case, x = 67kg, μ = 63kg, and σ = 17kg. Substituting these values into the formula, we get z = (67 - 63) / 17 = 0.235. Using a standard normal distribution table or calculator, we can find the area to the right of this z-score, which represents the proportion of children weighing greater than 67kg.

From the standard normal distribution table, we can determine that the area to the right of a z-score of 0.235 is approximately 0.4082. Multiplying this proportion by the total number of children (1,000), we find that there are approximately 408 children who weigh greater than 67kg.

Therefore, there are approximately 408 children who weigh greater than 67kg.

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