Question

18 months, mean = 85 words, standard deviation = 80 words

24 months, mean = 275 words, standard deviation = 120 words

Miku (who is 18 months old) has a vocabulary of 93 words, while Tessa (who is 24 months old) has a vocabulary of 287 words.
Relative to their age, who has a larger vocabulary?

O Miku
O Tessa
O Miku and Tessa have equally sized vocabularies relative to their ages.
O It's impossible to say without seeing all of the individual vocabulary sizes.

Answer 1

Miku and Tessa both have a Z-score of 0.1, indicating they have equally sized vocabularies relative to the average for their respective age groups. option a is correct.

Step-by-step explanation:

To determine who has a larger vocabulary relative to their age between Miku (18 months old) and Tessa (24 months old), we can calculate each child's standard score (Z-score). This score indicates how many standard deviations an individual's vocabulary size is from the mean of their age group.

The formula for calculating the Z-score is:

Z = (X - μ) / σ

For Miku: Z = (93 words - 85 words mean) / 80 words standard deviation = 0.1

For Tessa: Z = (287 words - 275 words mean) / 120 words standard deviation = 0.1

Both Miku and Tessa have a Z-score of 0.1, which means that their vocabulary sizes are both 0.1 standard deviations above the mean for their respective age groups. Therefore, relative to their ages, Miku and Tessa have equally sized vocabularies.