A) What fraction of kindergarten kids are expected to be less than 38 inches tal

Question

A) What fraction of kindergarten kids are expected to be less than 38 inches tall? B) in what height interval should the company expect to find the middle 70% of kindergarteners? C) at least how tall are the biggest 20% of kindergarteners? D) the biggest 20% of kindergarteners are expected to be at least how many inches tall? Question Help * Comparies 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 kindergarien kids should the company expect to be less than 38 inches tal? About%or kindergarten kids are expected to be less han 38 inches tal Round to one decimal place as needed.) b)In what height interval should the company expect to fndte middie 70% of kndergateners? The middie 70% of kindergarteners are expected to be betweeninches wdinches. (Use ascending order. Round to one decimal place as needed.) c)Atleast how tall aru biggest 20% of kndergarteners? The biggest 20% of kirdergarteners aro expected to be at leastinches tal Round to one decimal place as needed.) Enter your answer in each of the answer boxes 6 8 2 3

Explanation / Answer

Z = (X - 39.2)/1.9

A) What fraction of kindergarten kids are expected to be less than 38 inches tall?

P(X < 38) = P(Z < (38-39.2)/1.9)

=P(Z< -0.63) = 0.2643

B) in what height interval should the company expect to find the middle 70% of kindergarteners?

P(Z < z*) = 0.7/2 +0.5 =0.85

z* = 1.036

X1* = 39.2 +1.036 *1.9 = 41.1684

X2* = 39.2 -  1.036 *1.9 = 37.2316

hence 70 % lies between

(37.2316, 41.1684)

C) at least how tall are the biggest 20% of kindergarteners?

P(Z > z*) = 0.2

z* = 0.841

X* = 39.2 +0.841 *1.9 = 40.7979

D) the biggest 20% of kindergarteners are expected to be at least how many inches tall?

same as C) 40.7979

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