A nationwide survey of 100 boys and 50 girls in the first grade found that the daily average number of boys who are absent from

Question

17 days ago

6

A nationwide survey of 100 boys and 50 girls in the first grade found that the daily average number of boys who are absent from

school is 15, with a standard deviation of 7. For girls, the average number of absentees is 10, with a standard deviation of 6. The standard deviation of the difference is

Mathematics

2 answers:

Leona [9.2K] · Answer 1 · 2026-03-11T02:34:03+03:00

Leona [9.2K]17 days ago

6 0

The formula to calculate the difference between two standard deviations of populations n1 and n2 is:
sigma (difference)=√(sigma1/n1 + sigma2/n2). For this scenario:

sigma(d)= √(49/100 + 36/50)

Thus, the calculated standard deviation of the difference equals 1.1.

Leona [9.2K] · Answer 2 · 2026-03-11T02:34:27+03:00

Calculate the mean difference (male absences compared to female absences) within the population.

μd = μ1 - μ2 = 15 - 10 = 5

Determine the standard deviation of the difference.

σd = sqrt( σ12 / n1 + σ22 / n2 )

σd = sqrt(72/100 + 62/50) = sqrt(49/100 + 36/50) = sqrt(0.49 + 0.72) = sqrt(1.21) = 1.1

Calculate the z-score for when boys have three more absence days than girls. The difference between male and female absences is three in this situation. The corresponding z-score is

z = (x - μ)/σ = (3 - 5)/1.1 = -2/1.1 = -1.818

Determine the probability. We need to find the likelihood that the average absences from the male sample minus the average from the female sample is less than 3. Inputting the z-score (-1.818) into Stat Trek's Normal Distribution Calculator shows that the probability of a z-score being -1.818 or lower is approximately 0.035.