2. Suppose that the heights of kindergarten children are approximately normally

Question

2. Suppose that the heights of kindergarten children are approximately normally distributed with a mean of 42 inches and a standard deviation of 2.5 inches. a. How tall would a kindergartener be to be in the 90 percentile? Show your wowk (This is a "reverse look-up" problem) Label the axis with x and label the center with the value of . Label the axis with z and label the center with the value of O Show what area would represent the 90 percentile Shade in the area you are working with . Height b. What proportion of kindergarteners are between 40 and 45 inches tall? The proportion of kindergarteners are between 40 and 45 inches tall is

Explanation / Answer

mean = 42 , sd = 2.5
a)
P(X < x) = 0.90
P(Z < z) = 0.90
z = 1.282
X = mean + z *sd
= 42 + 1.282 * 2.5
= 45.205

b)
P( 40 < X< 45)
= P ( 0.8<Z<1.2 )=0.673

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