How do I find the the answer to B and C? My tables don\'t have 60% Companies who

Question

How do I find the the answer to B and C? My tables don't have 60%

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 39 inches tall? About 45.6% of kindergarten kids are expected to be less than 39 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 inches and inches (Use ascending order. Round to one decimal place as needed.) c) At least how tall are the biggest 25% of kindergarteners? The biggest 25% of kindergarteners are expected to be at least inches tall. Round to one decimal place as needed)

Explanation / Answer

A) P(X < 39)

= P((x - mean)/SD < (39 - mean)/SD)

= P(Z < (39 - 39.2)/1.9)

= P(Z < -0.11)

= 0.4562 = 45.62%

B) Z0.2 = 0.84

Mean +/- z0.2 * SD

= 39.2 +/- 0.84 * 1.9

= 39.2 +/- 1.6

= 37.6, 40.8

C) P(X > x) = 0.25

Or, P((X - mean)/SD > (x - mean)/SD) = 0.25

Or, P(Z > (x - 39.2)/1.9) = 0.25

Or, P(Z < (x - 39.2)/1.9) = 0.75

Or, (x - 39.2)/1.9 = 0.67

Or, x = 0.67 * 1.9 + 39.2

Or, x = 40.473 = 40.5

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