Question

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Answer 1

47.5% of students fall within heights of 100 cm to 120 cm

Explanation:

We are given that heights of Grade 1 students are normally distributed

Mean =
`\mu = 100 cm`

Standard deviation =
`\sigma = 10 cm`

a)

Empirical rule

68% of data lies within the first standard deviation from the mean i.e
`.(\mu-\sigma , \mu+\sigma)=(100-10,100+10)=(90,110)`

95% of all the data will fall within two standard deviations i.e.
`(\mu-2\sigma , \mu+2\sigma)=(100-2(10),100+2(10))=(80,120)`

99.7% of data lies within the three standard deviations i.e.
`( \mu - 3 \sigma , \mu +3 \sigma)=(100-3(10),100+3(10))=(70,130)`

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 =
`(1)/(2) * 95\% = 47.5\%`

Hence 47.5% of students fall within heights of 100 cm to 120 cm