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 (is 977 the correct answer?)

2.between 25 kg to 58kg (is 995 the correct answer?)

using z table

Answer 1

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

by the empirical rule 95% fall within 2 standard deviations of the mean

Pr(<55) = 95 = 2.5 =97.5%

97.5% of 1,000 = 975

but that's "just" a close estimate

for a more precise estimate use z tables or a z calculator

1-.02275 = 0.97725%

times 1000 = 977.25

round off to nearest integer = 977

Pr(25<x<58) involves two z scores

(25-45)/5 =-20/5=-4

P(25<x<45) = 49.997%

(58-45)/5= 2.6

P(45<x<58) =49.534%

P(25<x<58) = 49.997+49.634 = 99.531%

99.531% times 1000 = 995.31

rounded off to nearest integer = 995