Answer:
The no. of boys = 20
The no. of girls = 12
Step-by-step explanation:
Ratio of no. of boys to girls = 5 : 3
[5 multiplied with something, and 3 multiplied with something, added together makes 32.Thus, that something = x]
5x + 3x = 32
= 8x = 32
=x = 32÷8 = 4
5x = 5 x 4 = 20
3x = 3 x 4 = 12
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To solve this problem, we make use of the z statistic.
The formula for the confidence interval can be calculated using the formula:
Confidence Interval = p ± MOE
where,
p is the portion of girls = 278 / 556 = 0.5
MOE is the margin of error
We calculate the margin of error using the formula:
MOE = z * sqrt[p (1 – p) / n]
From the standard distribution tables, the value of z at 99% confidence is:
z = 2.58
Therefore the MOE is:
MOE = 2.58 * sqrt[0.5 (0.5) / 556]
MOE = 0.055
Therefore the confidence interval is:
Confidence Interval = 0.5 ± 0.055
Confidence Interval = 0.445, 0.555
0.445<p<0.555
