Question

Suppose birth weights for boys are approximately normal with a mean of 3.41 kg and a standard deviation of 0.55 kg. Max's parents are told that their newborn son falls at the 96th percentile. How much does Max weigh?

A) 4.32 kg
B) 3.95 kg
C) 3.20 kg
D) 4.75 kg

Answer 1

To find how much Max weighs, we need to convert the given percentile to a z-score. Using the formula z = (x - mean) / standard deviation, we calculate the z-score corresponding to the 96th percentile and solve for x to find Max's weight.

Step-by-step explanation:

To find how much Max weighs, we need to convert the given percentile to a z-score. A z-score indicates the number of standard deviations a value is away from the mean. Since Max falls at the 96th percentile, this means he is heavier than 96% of newborn boys. To find the z-score, we can use the formula: z = (x - μ) / σ, where x is Max's weight, μ is the mean, and σ is the standard deviation.

Let's calculate the z-score:

z = (x - 3.41) / 0.55

Since 96% falls to the right of the z-score, we can use the z-score table or calculator to find the z-score that corresponds to the 96th percentile. The z-score is approximately 1.75.

Substituting the z-score back into the formula, we can solve for x:

1.75 = (x - 3.41) / 0.55

Solving for x, we get:

x = 1.75 * 0.55 + 3.41

x = 4.32 kg

Therefore, Max weighs approximately 4.32 kg. that is option B