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April 2nd, 2017, 12:11 PM   #1
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Help solving a problem, is an example problem to understand

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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April 2nd, 2017, 12:13 PM   #2
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this is about as straightforward a normal distribution problem gets.

What specific issues are you having solving it?
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April 2nd, 2017, 03:28 PM   #3
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I'm taking it online and its difficult. Just an example to begin setting it up would help. I realized online classes are not best for me. My online homework guide doesn't lay things out clearly
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April 2nd, 2017, 03:54 PM   #4
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Quote:
Originally Posted by redsaints2010 View Post
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?
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.



$P[\text{boy's height } \geq 54]= 1 - P[\text{boy's height } < 54] =
1 - \Phi\left(\dfrac{54-55.5}{2.7}\right) = 1 - \Phi(-0.556) \approx 1- 0.289 = 0.711 = 71.1\%$

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

(c) you might have to think about a bit
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April 2nd, 2017, 04:17 PM   #5
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Where did the .289 come from? Thank you for the help
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April 2nd, 2017, 04:19 PM   #6
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Quote:
Originally Posted by redsaints2010 View Post
Where did the .289 come from? Thank you for the help
$\Phi(x)$ is the CDF of the standard normal, i.e. mean=0, std=1

It's the table that's in your book for solving these sorts of problems.
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April 2nd, 2017, 04:41 PM   #7
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Thank you
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