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 1.9inches. a) What fraction of kindergarten kids should the company expect to be less than 36 inches tall? About 48.4% of kindergarten kids are expected to be less than 36 inches tall. (Round to one decimal place as needed.) b) In what height interval should the company expect to find the middle 60% of kindergarteners? The middle 60% of kindergarteners are expected to be between nothing inches and nothing inches. (Use ascending order. Round to one decimal place as needed.) c) At least how tall are the biggest 10% of kindergarteners? The biggest 10% of kindergarteners are expected to be at least nothing inches tall.

Explanation / Answer

b. P(x1<x<x2)=0.60

Using z test we get

Using z distribution we get P(z1<z<z2)=0.60 for z=+/-0.841

So z1=x1-39.2/1.9=-0.841

For x1=37.60 and x2=40.80

c. P(X>=x)=0.10

Using z we get z=1.282

So x=41.64

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