Answer to Question #181455 in Statistics and Probability for Alice

Question #181455

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. What is the probability that a child picked at random has a height less than 104 cm?


1
Expert's answer
2021-05-03T04:44:15-0400

We assume normal distribution with the mean (μ\mu ) and standard deviation (σ\sigma ) which are given as follows



μ=110 cm and σ=6 cm .\mu =110 \text{ cm and } \sigma =6\text{ cm }.


Therefore,



P(x<104)=P(z<xμˉσ)=P(z<1041106),=P(z<66)=P(z<1)=0.15866.P (x < 104 ) = P (z<\frac{x-\bar{\mu}}{\sigma})=P(z<\frac{104-110}{6}),\\ =P(z<\frac{-6}{6})=P(z<-1)=0.15866.


Thus, the probability that a child picked at random has a height less than 104 cm is 0.15866.


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