MATH302 WEEK 3 DISCUSSION

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School

American Military University *

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302

Subject

Statistics

Date

Jan 9, 2024

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docx

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Uploaded by carelessvicki

Hello Class, Using my car data set from Week 2: Average for my car data set= 68026.5 Looking at my data set I see that 7 out of 100 cars fall below the average. This means that p=7/1=.70 and q=1-.70=.30 1. If you were to find another random sample of 10 cars based on the same data, what is the probability that exactly 4 of them will fall below the average? Make sure you interpret your results. Because of the word exactly I want to find this probability P(x=4). I will use the BINOM.DIST() function to find this probability. P(x=4)=BINOM.DIST(4,10,.70,FALSE) There is a 3.68% that exactly 4 of the cars will fall below the average. 2. If you were to find another random sample of 10 cars based on the same data, what is the probability that fewer than 5 of them will fall below the average? Make sure you interpret your results. Because of the word fewer I will use the less than sign. The probability I want to find is P(x<5) This probability is in the less than form NOT the less than or equal to form so I need to rewrite this in the less than or equal to from. P(x<5)=P(x<=-1)=P(x<=4) Now that the probability is in the less than or equal to form, I will input into Excel. P(<5)=BINOM.DIST(4,10,.70,TRUE) There is a 4.73% that fewer than 5 of the cars will fall below the average. 3. If you were to find another random sample of 10 cars based on the same data, what is the probability that more than 6 of them will fall below the average? Make sure you interpret your results. Because of the word more I will use the greater than sign. The probability I want to find is P(x>6)

This probability is in the greater than form NOT the less than or equal to form so I need to re- write this in the less than or equal to form. P(x>6)=1-p(x=<=6)=1-P(x=<5) Now that the probability is in the less than or equal to form I will input into Excel =BINOM.DIST(6,10,0.7,TRUE) There is a 35.04% probability that more than 6 of the cars will fall below the average. 4. If you were to find another random sample of 10 cars based on the same data, what is the probability that at least 4 of them will fall below the average? Make sure you interpret your results. Because of the words at least I use the greater than or equal to sign. The probability I want to find is P(x=.4) I need to rewrite the from in the less than or equal to from. Px=>4=1-P(x=<4-1)=1-P(x=<3) Now I can input into Excel =BINOM.DIST(6,10,0.7,TRUE) There is 1.06% probability that at least 4 of cars will fall below the average. -V

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