Needs to Done on Time!!!
Q1
Probability of success on a single trial | 60% | ||
Number of trials | 18 | ||
Number of successes (x) | |||
Binomial probability: | |||
1 | P(X >=8) | 0.8653 | =1-BINOMDIST(8,B2,B1,TRUE) |
2 | P(X = 10) | 0.1734 | =BINOMDIST(10,B2,B1,FALSE) |
3 | P(X = 5) | 0.0045 | =BINOMDIST(5,B2,B1,FALSE) |
4 | P(X >=15) | 0.0082 | =1-BINOMDIST(15,B2,B1,TRUE) |
5 | The expected number of acceptances. | 10.8000 | =B2*B1 |
6 | the standard deviation | 2.0785 | =SQRT(C9*(1-B1)) |
Q2
x = critical value | 71 | ||
u = mean | 80 | ||
s = standard deviation | 6 | ||
Z | -1.5 | =(C1-C2)/C3 | |
Thus, using a table/technology, the right tailed area of this is | |||
7 | P(z > -1.5 ) | 0.9332 | =1-NORMSDIST(C4) |
We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as | |||
x1 = lower bound | 89 | ||
x2 = upper bound | 92 | ||
z1 = lower z score | 1.5 | =(C9-C2)/C3 | |
z2 = upper z score | 2 | =(C10-C2)/C3 | |
P(z < z1) | 0.9331927987 | =NORMSDIST(C11) | |
P(z < z2) | 0.9772498681 | =NORMSDIST(C12) | |
Thus, the area between them, by subtracting these areas, is | |||
8 | P(z1 < z < z2) | 0.0441 | =C14-C13 |
Then, using table or technology, | |||
P | 2.50% | ||
9 | x = critical value | 91.76 | [lowest score with merit] |
=1.96*C3+C2 |
Business Major
School Type | Cost | 30 Year ROI | Annual ROI | Annual ROI (Business Major) | Annual ROI (Engineering Major) | ||
Private | $222,700.00 | $1,786,000.00 | 7.70% | ||||
Private | $176,400.00 | $1,758,000.00 | 8.40% | Mean | 7.82% | 9.15% | |
Private | $212,200.00 | $1,714,000.00 | 7.80% | Standard Error | 0.25% | 0.33% | |
Public | $125,100.00 | $1,535,000.00 | 9.10% | Median | 7.35% | 8.50% | |
Private | $212,700.00 | $1,529,000.00 | 7.40% | Mode | 7.00% | 7.90% | |
Public | $92,910.00 | $1,501,000.00 | 10.10% | Standard Deviation | 1.10% | 1.46% | |
Private | $214,900.00 | $1,485,000.00 | 7.30% | Sample Variance | 0.01% | 0.02% | |
Private | $217,800.00 | $1,483,000.00 | 7.20% | Kurtosis | 0.2120 | -1.3960 | |
Private | $225,600.00 | $1,444,000.00 | 7.00% | Skewness | 1.2333 | 0.4731 | |
Private | $217,300.00 | $1,442,000.00 | 7.10% | Range | 3.40% | 4.20% | |
Private | $226,500.00 | $1,441,000.00 | 7.00% | Minimum | 6.70% | 7.50% | |
Private | $215,500.00 | $1,438,000.00 | 7.20% | Maximum | 10.10% | 11.70% | |
Private | $223,500.00 | $1,428,000.00 | 7.00% | Sum | 156.40% | 182.90% | |
Private | $226,600.00 | $1,414,000.00 | 7.00% | Count | 20 | 20 | |
Private | $189,300.00 | $1,397,000.00 | 7.50% | ||||
Public | $89,700.00 | $1,382,000.00 | 9.90% | BIN | Frequency | ||
Public | $87,030.00 | $1,376,000.00 | 10.00% | 6.5%-7.5% | 6 | ||
Private | $218,200.00 | $1,343,000.00 | 6.90% | 7.5%-8% | 6 | ||
Private | $229,900.00 | $1,339,000.00 | 6.70% | 8%-8.5% | 2 | ||
Private | $148,800.00 | $1,321,000.00 | 8.10% | 8.5%-9% | 2 | ||
Best College ROI by Majo 2013: Payscale.com | 9%-9.5% | 0 | |||||
9.5%-10% | 1 | ||||||
10%-10.5% | 2 | ||||||
>10.5% | 1 |
Histogram:Business Major
6.5%-7.5% 7.5%-8% 8%-8.5% 8.5%-9% 9%-9.5% 9.5%-10% 10%-10.5% > 10.5% 6 6 2 2 0 1 2 1BIN
Frequency
Engineering Major
School Type | Cost | 30 Year ROI | Annual ROI | Annual ROI (Engineering Major) | ||
Private | $221,700.00 | $2,412,000.00 | 8.70% | |||
Private | $213,000.00 | $2,064,000.00 | 8.30% | Mean | 9.15% | |
Private | $230,100.00 | $1,949,000.00 | 7.90% | Standard Error | 0.33% | |
Private | $222,600.00 | $1,947,000.00 | 8.00% | Median | 8.50% | |
Private | $225,800.00 | $1,938,000.00 | 8.00% | Mode | 7.90% | |
Public | $87,660.00 | $1,937,000.00 | 11.20% | Standard Deviation | 1.46% | |
Private | $224,900.00 | $1,915,000.00 | 7.90% | Sample Variance | 0.02% | |
Private | $221,600.00 | $1,878,000.00 | 7.90% | Kurtosis | -139.60% | |
Public | $125,100.00 | $1,854,000.00 | 9.80% | Skewness | 47.31% | |
Private | $215,700.00 | $1,794,000.00 | 7.90% | Range | 4.20% | |
Public | $92,530.00 | $1,761,000.00 | 10.60% | Minimum | 7.50% | |
Private | $217,800.00 | $1,752,000.00 | 7.70% | Maximum | 11.70% | |
Public | $89,700.00 | $1,727,000.00 | 10.70% | Sum | 182.90% | |
Private | $229,600.00 | $1,716,000.00 | 7.50% | Count | 20 | |
Public | $101,500.00 | $1,703,000.00 | 10.20% | |||
Public | $115,500.00 | $1,694,000.00 | 9.70% | |||
Public | $104,500.00 | $1,690,000.00 | 10.10% | Engineering Major | ||
Public | $69,980.00 | $1,685,000.00 | 11.50% | BIN | Frequency | |
Private | $219,400.00 | $1,676,000.00 | 7.60% | 7%-7.5% | 1 | |
Public | $64,930.00 | $1,668,000.00 | 11.70% | 8%-8.5% | 8 | |
8.5%-9% | 1 | |||||
9%-9.5% | 1 | |||||
9.5%-10% | 0 | |||||
10%-10.5% | 2 | |||||
10.5%-11% | 2 | |||||
11%-11.5% | 2 | |||||
11.5%-12% | 3 | |||||
12%-12.5% | 1 | |||||
Histogram:Engineering Major
7%-7.5% 8%-8.5% 8.5%-9% 9%-9.5% 9.5%-10% 10%-10.5% 10.5%-11% 11%-11.5% 11.5%-12% 1 8 1 1 0 2 2 2 3BIN
Frequency