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.below 55 kg

2.between 25 kg to 58kg

Answer 1

mean =45

SD = 5

z = (55-45)/5 =10/5 = 2

55 is 2 Standard Deviations above the mean

use the empirical rule: 68-95-99.7% for 1,2 and 3 SD

estimate is 0.97.5% of the weights fall below 2 Standard Deviations above the mean

95+(1-95)/2=95+5/2 = 95+2.5 = 97

0.975 times 1,000 = 975 children weigh less than 55 kg

for 25 to 45

z= (25-45)/5 =-20/5 = -4 or 4 SD below the mean. That's about 99.9% from 25 to 65

and 99.9/2 = 49.95% from 25 to 45

for 58

z = (58-45)/5 =13/5 = 2.6 SD above the mean

that's somewhere between 95 and 99.7 between 32 and 45

and between 95/2 and 99.7/2 = 47.5 and 49.85 between 45 and 58

47.5+49.85)/2 = about 49%

add 49 to 50 = 99% between 25 to 58

.99 time 1,000 = estimated 990 children between 25 and 58 kg