Question

A person's intelligence quotient (i) is found by dividing mental age (m), as indicated by standard tests, by chronological age (c), and then multiplying this ratio by 100. the formula i = 100m c can be used. if the i range of a group of 12-year-olds is given by 80 ≤ i ≤ 120, find the range of the mental age of this group. (enter your answers from lowest to highest.)

Answer 1

The range of the mental age for a group of 12-year-olds with an IQ range of 80 to 120 is from 9.6 to 14.4 years, found by using the formula i = 100m/c.

Step-by-step explanation:

To find the range of the mental age (m) for a group of 12-year-olds with an IQ range of 80 to 120, we use the formula i = 100m/c. In this formula, i stands for intelligence quotient, m stands for mental age, and c stands for chronological age. Since the chronological age (c) for the group is 12, we will rearrange the formula to solve for m: m = i × c / 100.

To find the minimum mental age (m), we use the lowest IQ value from the given range:

• m = 80 × 12 / 100
• m = 960 / 100
• m = 9.6 years

To find the maximum mental age (m), we use the highest IQ value from the given range:

• m = 120 × 12 / 100
• m = 1440 / 100
• m = 14.4 years

Therefore, the range of the mental age for this group of 12-year-olds is from 9.6 to 14.4 years.

Answer 2

`9.6 \leqslant m \leqslant 14.4`
i = (100m)/c
lowest i = 80, highest i = 120
c = 12
this will result in 2 equations, one will be the lowest (solving m when i = 80), and the highest (solving m when i = 120)
solve m when i = 80:
i = (100m)/c
80 = (100m)/12
80×12 = 100m
960 = 100m
960/100 = m
9.6 = m
solve m when i = 120:
i = (100m)/c
120 = (100m)/12
120×12 = 100m
1440 = 100m
1440/100 = m
14.4 = m
therefore,

`9.6 \leqslant m \leqslant 14.4`