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Home Q & A Board Science-Related Homework Help Mathematics
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garymiller28602 garymiller28602
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7 years ago
In order to ride in a car at the Tomorrowland Speedway at Magic Kingdom, you must be at least 32 inches tall.  To drive a car at the Tomorrowland Speedway, you must be at least 54 inches tall.  Assume 5th graders heights are normally distributed.  The mean height for female 5th graders is 54.4 inches with a standard deviation of 2.7 inches.  The mean height for male 5th graders is 55.5 inches with a standard deviation of 2.7 inches.  For each of the following, draw a sketch of the situation, shade the appropriate area, and round your percentage to the nearest hundredths.

a.   What percent of 5th grade boys can drive a car at the Tomorrowland Speedway?             
 
 
 
 b.   What percent of 5th grade girls can drive a car at the Tomorrowland Speedway?             
 
 
 
 
 
c.   If the creators of the Tomorrowland Speedway want to change the height requirement to allow the tallest 90% of 5th grade boys to drive a car, what should the new height requirement be?
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#1
Staff Member
6 years ago
boys are distributed as N(55.5,2.7)

In order to drive the car you must be 54 inches tall. So we want the percentage of boys who are 54 or greater inches tall.

Φ(x) is the CDF of the standard normal, i.e. mean=0, std=1

P[boy's height ≥54]=1−P[boy's height <54]=1−Φ(54−55.5/2.7)=1−Φ(−0.556)≈1−0.289=0.711=71.1%

using this you should be able to do (b) w/o much trouble
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