Due Sat 09/30/2017 11:59 p Heights of 10 year olds, regardless of gender, closel

Question

Due Sat 09/30/2017 11:59 p Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. (a) What is the probability that a randomly chosen 10 year old is shorter than 46 inches? (b) What is the probability that a randomly chosen 10 year old is betwen 61 and 67 inches? (c) If the tallest 10 % of the class is considered "very tall", what is the height cutoff for "very tall"? (d) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What of 10 year olds cannot go on this ride? percent

Explanation / Answer

Mean is 55 and SD is 6. z is calculated as (x-mean)/sd where x is given

a) P(x<46)= P(z<(46-55)/6)=P(z<-1.5) =1-P(z<1.5). from normal distribution table, look for the area under the curve as 1.5 in the leftmost column and 0.00 in the top most row. thus it is 1-0.9332=0.0668

b) P(61<x<67)=P((61-55)/6<z<(67-55)/6)=P(1<z<2)=P(z<2)-P(z<1). form normal distribution table we get 0.9772-0.8413=0.1359

c) P(x<X)=0.9 (tallest 10% represents the limit of 90% of population below it)

from normal distribution table we get (x-55)/6=1.28 (z value corresponding to area of 0.8997 since it is closest to 0.9)

thus x=1.28*6+55=62.68

d) P(x<54) cannot go since they are shorter than 54

thus P(z<(54-55)/6)=P(z<-1.67) or 1-P(z<1.67)

thus, from normal distribution table we get 1-0.9525 =0.0475

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