Companies who design furniture for elementary school classrooms produce a variet

Question

Companies who design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 39.2 inches and standard deviation of 1.9 inches. What fraction of kindergarten kids should the company expect to be less than 38 inches tall? About 26.4% of kindergarten kids are expected to be less than 38 inches tall. (Round to one decimal place as needed.) In what height interval should the company expect to find the middle 90% of kindergarteners? The middle 90% of kindergarteners are expected to be between ___ inches and ___ inches. (Use ascending order. Round to one decimal place is needed.)

Explanation / Answer

a) P(X<38)=P(Z<(38-39.2)/1.9)=P(Z<-0.6316)=0.264 ~ 26.4%

b) for 90% ; z=1.645

therefore middle 90% values =mean -/+ z*std deviation =39.2 -/+ 1.645*1.9 =36.1 inches and 42.3 inches

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