10 pages/≈2750 words
Mathematics & Economics
Module 3 Case Frequency Distribitions (Math Problem Sample)
All problems need to include all required steps and answers and all answers need to be reduced to the lowest terms. Please see instructions.source..
TITLE OF PROJECT
1 The math grades on the final exam varied greatly. Using the scores below, how many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
1 34Â Â Â 86Â Â Â 57Â Â Â 73Â Â Â 85Â Â Â 91Â Â Â 93Â Â Â 46Â Â Â 96Â Â Â 88Â Â Â 79Â Â Â 68Â Â Â 85Â Â Â 89
To answer this item, first we need to compute for standard deviation. We will use this formula.
We will compute this formula in 4 steps.
Step 1: Find the mean.
Mean = (99+34+86+57+73+85+91+93+46+96+88+79+68+85+89) / 15
Mean = 77.9333.
Step 2:Â Create the following table.
(data - mean)2
Step 3:Â Find the sum of numbers in the last column to get.
Step 4:Â CalculateÂ ÏƒÂ using the above formula.
Using the mean and standard deviation of these scores we can now get the z-score for each grade using this formula:
Z value = (X - Âµ) / Ïƒ
Where, X = Standardized Random Variable,
Âµ = Sample Mean,
Ïƒ = Sample Standard Deviation.
The table below summarizes the z-score for each math grade
There are 11 math grades that are within one (1) standard deviation away from the mean while 14 math grades are within two (2) standard deviations away from the mean. All math grades are within three (3) standard deviations away from the mean.
1 The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
Step 1: Sketch the curve.
The probability thatÂ X>85Â is equal to the blue area under the curve.
SinceÂ Î¼=74.8Â andÂ Ïƒ=7.57Â we have:
PÂ (Â X>85Â )=PÂ (Â Xâ€’Î¼>85â€’74.8Â )=PÂ (Â Xâ€’Î¼Ïƒ>85â€’74.87.57)
SinceÂ Z=xâ€’Î¼ÏƒÂ andÂ 85â€’74.87.57=1.35Â we have:
PÂ (Â X>85Â )=PÂ (Â Z>1.35Â )
Step 3:Â Use the standard normal table to conclude that:
0.0885 x 100 = 8.85%
Only 8.85% of the class (or one person) scored above 85% for Math test #3.
2 If you know the standard deviation, how do you find the variance?
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