Answer:
47.5% of students fall within heights of 100 cm to 120 cm
Step-by-step explanation:
We are given that heights of Grade 1 students are normally distributed
Mean = [tex]\mu = 100 cm[/tex]
Standard deviation = [tex]\sigma = 10 cm[/tex]
a)
Empirical rule
68% of data lies within the first standard deviation from the mean i.e[tex].(\mu-\sigma , \mu+\sigma)=(100-10,100+10)=(90,110)[/tex]
95% of all the data will fall within two standard deviations i.e.[tex](\mu-2\sigma , \mu+2\sigma)=(100-2(10),100+2(10))=(80,120)[/tex]
99.7% of data lies within the three standard deviations i.e.[tex]( \mu - 3 \sigma , \mu +3 \sigma)=(100-3(10),100+3(10))=(70,130)[/tex]
b)Percentage of students fall within heights of 100 cm to 120 cm
Using the normal distribution curve
Percentage of students fall within heights of 100 cm to 120 cm = [tex]\frac{1}{2} \times 95\% = 47.5\%[/tex]
Hence 47.5% of students fall within heights of 100 cm to 120 cm
