Statistics Practice Questions

Required total points = 3.5*5=17.5
Actual total points (4 subjects) = 2*3.7 + 3.3 + 3 = 13.7
Required total points for the last subject = 17.5 - 13.7 = 3.8
He has to get a minimum of 3.8 points or Grade A (that is 4 points). (Getting A-, 3.7 GPA, won't be enough to get an overall minimum GPA of 3.5 for the 5 subjects)
The correct answer is A.

2002 total = 60, mean = 15, in 2003, total = 72, mean = 18, from 15 to 18, increase = 20%
Answer is 20%

The original average price of the 5 stocks is:
\[ \frac{20 + 35 + 40 + 45 + 70}{5} = \frac{210}{5} = \$42 \]
An approximately 2% increase would give a new average of about \( \$42.84 \), so the new total would be about \( \$214.20 \).

Since one stock increased by 15% and one decreased by 35%, while three remained constant, we can express the net change as:
\[ 0.15P - 0.35Q \]
where \( P \) is the price of the stock that increased and \( Q \) is the price of the stock that decreased.

For the average to increase, we need \( 0.15P - 0.35Q > 0 \), which means \( 0.15P > 0.35Q \), or \( P > 2.33Q \).

This inequality tells us that the increasing stock must have a price more than 2.33 times that of the decreasing stock. Examining the possible combinations:
- If \( P = \$70 \): We need \( Q < 70/2.33 \approx \$30 \), so \( Q \) could only be \( \$20 \).
- If \( P = \$45 \): We need \( Q < 45/2.33 \approx \$19.3 \), but the minimum stock price is \( \$20 \), so no valid \( Q \) exists.
- For any \( P \leq \$45 \), the required \( Q \) would be too small to match any available stock price.

Therefore, the only possible combination is \( P = \$70 \) (increasing by 15%) and \( Q = \$20 \) (decreasing by 35%).

Verification:
New total \( = 20 \times 0.65 + 35 + 40 + 45 + 70 \times 1.15 = 13 + 35 + 40 + 45 + 80.5 = \$213.50 \)
New average \( = 213.50/5 = \$42.70 \)
Percent change \( = \frac{42.70 - 42}{42} \times 100 \approx 1.67\% \approx 2\% \)

This confirms that \( \$70 \) increased by 15%, \( \$20 \) decreased by 35%, and the stocks that remained constant are \( \$35 \), \( \$40 \), and \( \$45 \).

The correct answer is E.