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 20. The formula $I = \frac { 20 \mathrm { M } } { C }$ can be used. If the I range of a group of 12-year-olds is given by $76 \leq I \leq 189$ , find the range of the mental age of this group.
A) $3.8 \leq M \leq 9.45$
B) $912 \leq M \leq 2268$
C) $76 \leq M \leq 189$
D) $45.6 \leq M \leq 113.4$
E) $91.2 \leq M \leq 226.8$

Question

Quizplus · Accepted Answer

To find the range of the mental age (M) for the group of 12-year-olds, we use the given formula $I = \frac { 20M } { C }$ and the provided IQ range $76 \leq I \leq 189$. Since the chronological age (C) is 12 for this group, we substitute C = 12 into the formula and solve for M in the given IQ range:For the lower limit, $76 = \frac{20M}{12}$, solving for M gives $M = \frac{76 \times 12}{20} = 45.6$.For the upper limit, $189 = \frac{20M}{12}$, solving for M gives $M = \frac{189 \times 12}{20} = 113.4$.Therefore, the range of the mental age for this group is $45.6 \leq M \leq 113.4$.

A Person S Intelligence Quotient ( I ) Is Found I=20MCI = \frac { 20 \mathrm { M } } { C }I=C20M​

A Person S Intelligence Quotient ( I ) Is Found $I = \frac { 20 \mathrm { M } } { C }$