Question #181452

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. How many children have heights between 98 cm and 104 cm?


1
Expert's answer
2021-04-29T18:00:16-0400

mean =μ=110= \mu = 110

standard deviation =σ=6= \sigma = 6

P(98<x<104)=P(981106<Z<1041106)=P(2<Z<1)=P(Z<1)P(Z<2)=0.15860.0227=0.1359P(98<x<104) = P(\frac{98-110}{6}<Z< \frac{104-110}{6}) \\ = P(-2 <Z< -1) \\ = P(Z< -1) -P(Z< -2) \\ = 0.1586 – 0.0227 \\ = 0.1359

= 13.59 %

500×0.1359=68500 \times 0.1359 = 68 children have heights between 98 cm and 104 cm


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