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Sagot :
EXPLANATION
First, we need to apply the z-score table as shown as follows:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where u=mean=71 inches , standard deviation=sigma= 4.5 inches.
We need to compute the Probability that the student's height fall between 61 and 70 inches.
P(61
In terms of z-score this would be:
P(61
Computing the z-score when x=61:
[tex]z=\frac{61-71}{4.5}=\frac{-10}{4.5}=-2.22[/tex]Computing the z-score when x=70:
[tex]z=\frac{70-71}{4.5}=\frac{1}{4.5}=-0.22[/tex]Now we need to look up z= -2.22 and z=-0.22 on a z-table.
The results are z_-2.22= 0.01321 and z_-0.22=0.41294
Subtracting both terms give us the probability that the heights fall between those numbers:
[tex]P(61This means there is a 0.39973 probability the students will be between 61 and 70 inches tall.. Since there are 1912 students at the school, the expected number of students who would be between 61 and 70 inches tall would be:[tex]1912\cdot0.39973=764.28376\approx764\text{ students}[/tex]
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