Math 205
Your Name: Jennifer Green MAT 205 Final Examination
Your Score: of 250 points
NOTE: You must show your work on each problem to receive full credit points allocated for each problem (excluding T/F questions)
Write a matrix to display the information.
1) At a store, Sam bought 3 batteries, 15 60-watt light bulbs, 46 100-watt light bulbs, 8 picture-hanging kits, and a hammer. Jennifer bought 12 batteries, 3 100-watt light bulbs, and a package of tacks. Write the information as a 2 x 6 matrix.
| |BATTERIES |60watt light bulbs |100 watt light bulbs |Picture hanging kits |Hammer |Package of tacks |
|Sam |3 |15 |46 |8 |1 |0 |
|Jennifer |12 |0 |3 |0 |0 |1 |
In a certain distribution, the mean is 50 with a standard deviation of 6. Use Chebyshev 's theorem to tell the probability that a number lies in the following interval. Round your results to the nearest whole percent.
2) Between 35 and 65
Ans: we have z = (35-50)/6 = -2.5 and z = (65-50)/6 = 2.5
So 35 and 65 lies within 2.5 standard deviation of mean
By Chebyshev’s theorem we have the probability as 1 -1/k2 , where k is the standard deviation within which the numbers
In this case k = 2.5
So the required probability = 1 -1/2.52
=> 0.84
=>at least 84%
A die is rolled five times and the number of twos that come up is tallied. Find the probability of getting the indicated result.
3) Two comes up one time.
Ans: This is an example of binomial distribution
Probability of occurance of 2, p = ½
Probability of non-occurrence of 2, q = 1-1/2 =1/2
So the probability that two comes 1 times (which means it doesn’t appear on other 4 occaisions) ⇨ C(5,1) p1q4 ⇨ 5(1/6)(5/6)4 ⇨
Your Score: of 250 points
NOTE: You must show your work on each problem to receive full credit points allocated for each problem (excluding T/F questions)
Write a matrix to display the information.
1) At a store, Sam bought 3 batteries, 15 60-watt light bulbs, 46 100-watt light bulbs, 8 picture-hanging kits, and a hammer. Jennifer bought 12 batteries, 3 100-watt light bulbs, and a package of tacks. Write the information as a 2 x 6 matrix.
| |BATTERIES |60watt light bulbs |100 watt light bulbs |Picture hanging kits |Hammer |Package of tacks |
|Sam |3 |15 |46 |8 |1 |0 |
|Jennifer |12 |0 |3 |0 |0 |1 |
In a certain distribution, the mean is 50 with a standard deviation of 6. Use Chebyshev 's theorem to tell the probability that a number lies in the following interval. Round your results to the nearest whole percent.
2) Between 35 and 65
Ans: we have z = (35-50)/6 = -2.5 and z = (65-50)/6 = 2.5
So 35 and 65 lies within 2.5 standard deviation of mean
By Chebyshev’s theorem we have the probability as 1 -1/k2 , where k is the standard deviation within which the numbers
In this case k = 2.5
So the required probability = 1 -1/2.52
=> 0.84
=>at least 84%
A die is rolled five times and the number of twos that come up is tallied. Find the probability of getting the indicated result.
3) Two comes up one time.
Ans: This is an example of binomial distribution
Probability of occurance of 2, p = ½
Probability of non-occurrence of 2, q = 1-1/2 =1/2
So the probability that two comes 1 times (which means it doesn’t appear on other 4 occaisions) ⇨ C(5,1) p1q4 ⇨ 5(1/6)(5/6)4 ⇨