The weights of 1000 children have an average of 45 kilograms and a standard deviation of 5 kilograms.

Question

Situation: You volunteered to be part of the medical mission in your barangay and in-charge to get weight of the children. The weights of 1000 children have an average of 45 kilograms and a standard deviation of 5 kilograms.

Estimate the range of the number of children weighing

1. 40 kg to 50 kg

2. below 55 kg

3. between 25 kg to 58kg

Answer 1

68% of 1,000 = 680 between 40 and 50 kg

below 55 kg is 2 standard deviations below the mean, 2.5% of 1,000 = 25 children

45-25)/5=20/5=4 standard deviations below the mean. that's nearly 50% to the left of the mean

to the right is

58-45)/5 = 13/5 = 2.6 standard deviations above the mean, between 2 and 3

2 above is 95%/2 = 47.5%, 3 above is 99.7%/2 = 49.85%

add that to 50% to get 97.5% to 99.85%,

estimate = about 99% of 1000 = 990 children between 25 and 58 kg

use the empirical rule 68-95-99.7% for 1,2 and 3 standard deviations from the mean

for more accurate calculations use a z calculator on line or z tables