Final answer:
The standard score for a three-year-old boy who is 99.5 cm tall is 0.78, which is option (d). This z-score indicates that the boy is 0.78 standard deviations above the average height for three-year-old boys.
Step-by-step explanation:
The question is asking to calculate the standard score (also known as a z-score) for a three-year-old boy who is 99.5 cm tall given the population mean of 96 cm and a standard deviation of 4.5 cm.
To find the z-score, you use the following formula:
z = (X - μ) / σ
Where:
X = value to convert into z-score (99.5 cm)
μ = mean (96 cm)
σ = standard deviation (4.5 cm)
Plugging in the numbers:
z = (99.5 - 96) / 4.5
z = 3.5 / 4.5
z = 0.78
So the correct answer is (d) 0.78.
This z-score tells us that the boy's height of 99.5 cm is 0.78 standard deviations above the mean.