Question

The perimeters of a certain kind of rectangles are bell-shaped symmetric with a mean of 40 cm and a standard deviation of 12 cm. Use the range rule of thumb to estimate the minimum and maximum "usual" values for perimeters of this kind of rectangles.

a) 16 cm, 64 cm
b) 18 cm, 66 cm
c) 28 cm, 52 cm
d) 15 cm, 65 cm

Answer 1

The estimated minimum and maximum usual values for the perimeters of rectangles with a mean perimeter of 40 cm and standard deviation of 12 cm are 16 cm and 64 cm, respectively, as per the range rule of thumb. So the correct answer is Option A.

Step-by-step explanation:

The question asks to estimate the minimum and maximum "usual" values for perimeters of a certain kind of rectangles using the range rule of thumb and given data where the mean perimeter is 40 cm with a standard deviation of 12 cm. According to the range rule of thumb, the "usual" range of data in a bell-shaped symmetric distribution is approximately within two standard deviations from the mean. To estimate this range:

• Calculate the lower bound by subtracting two standard deviations from the mean: 40 cm - (2 x 12 cm) = 16 cm.
• Calculate the upper bound by adding two standard deviations to the mean: 40 cm + (2 x 12 cm) = 64 cm.

Therefore, the estimated minimum and maximum "usual" values for the perimeters are 16 cm and 64 cm, respectively. The answer choice that matches these values is (a) 16 cm, 64 cm.