out otuile Claims 8. Companies that design furniture for elementary school class

Question

out otuile Claims 8. Companies that 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 38.2 inches and standard deviation of 18 inches. (a) What fraction of kindergarten kids should the company expect to be less than 3 feet tall? (b) In what height interval should the company expect to find the middle 80% of kindergarteners? (c) At least how tall are the biggest 10% of kindergartners?

Explanation / Answer

QUestion 8

Here mean height = 38.2 inches

standard deviation = 1.8 inches

(a) If x is the height of a random children

Pr(x < 3 feet ; 38.2 inch ; 1.8 inch)

Z = (36 - 38.2)/1.8 = -1.2222

Pr(x < 3 feet ; 38.2 inch ; 1.8 inch) = Pr(Z < -1.2222) = 0.1108

(b) Here middle interval where 80% of kids can be expected are can be calculated by 80% confidence interval

= 38.2 +- Z80% * s

= 38.2 +- 1.2816 * 1.8

= (35.9 inch, 40.5 inch)

9c) Here the biggest 10% height are H inch so

Pr(x < H ; 38.2 inch ; 1.8 inch) = 0.90

Z - value

Z = 1.2812

(H - 38.2)/1.8 = 1.2812

H = 40.5 inch.

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