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October 13th, 2012, 09:30 AM   #1
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question about statistics

If someone can help me with these problems in statistics that be great:

The time for the event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 60 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association?

the amount of soda a dispensing machine pours into 12-ounce can of soda follows a normal distribution with a standard deviation of 0.16 ounce. Every can that has more than 12.40 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that must be cleaned because of spillage to 3%?

Transportation officials tell us that 70% of drivers wear seat belts while driving. Find the probability that more than 579 drivers in a sample of 800 drivers wear seat belts.
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October 13th, 2012, 08:22 PM   #2
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Re: question about statistics

Hi jmersh, and welcome to the forums. I am by no means an expert as I am trying to learn myself. However, I will try:

For the first problem, we have to find the number of standard deviations below the mean where the Cumulative Distribution Function (CDF) = 0.1. Using an online calculator, http://www.mathsisfun.com/data/stand...ion-table.html and selecting "Up to Z", to get 10%, we need to go -1.28 standard deviations, which is 470-1.28(60)=393.2 seconds. A check with the complete CDF equation at http://www.wolframalpha.com/input/?i...860*2%5E0.5%29 yields a value close to 393.11 seconds, which is more accurate. The formula used may be found at http://en.wikipedia.org/wiki/Normal_distribution on the right side in CDF (under the graphs) . Obviously, you can use your own table if you have one.

I will let you try the second problem using similar techniques. If you get stuck, just post again and someone will help.

For the third problem, at http://en.wikipedia.org/wiki/Binomial_distribution under "Mean and variance" it says that the expected value is np=800*0.7=560 (which is obvious to me), and the variance=np(1-p)=800*0.7*(1-0.7)=168 (which is not obvious to me). The standard deviation is the square root of the variance = 12.961. So you can figure out how many standard deviations away 579+1=580 is from the expected value and go to the first link, click on "Z onwards" and set the value to the number of standard deviations and read off the percent (I got 1.54 standard deviations and 6.2%). Since this is new to me, I wrote a Ruby program to simulate this, and the probability, mean, and standard deviation values as simulated were close to those calculated.
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October 15th, 2012, 06:15 PM   #3
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Re: question about statistics

thanks! really appreciate it.
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