Question : P1 is the average of all prime numbers below 12 and P2 is the average of all prime numbers between 12 and 30. What is the value of 5P1 – P2?
Option 1: 7.8
Option 2: 8.6
Option 3: 9.8
Option 4: 7.5
Correct Answer: 7.8
Solution :
$P_1$ is the average of all prime numbers below 12
$P_2$ is the average of all prime numbers between 12 and 30
The prime number between 1 to 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Average = $\frac{\text{Sum of all observations}}{\text{Number of observations}}$
The average of prime no. below 12 is
Average ($P_1$) = $\frac{2+3+5+7+11}{5} = \frac{28}{5}$
The average of prime no. between 12 to 30,
Average ($P_2$) = $\frac{13+17+19+23+29}{5} = \frac{101}{5}$ = 20.2
The value of 5$P_1$ – $P_2$ = $5 \times \frac{28}{5} – 20.2$ = 28 – 20.2 = 7.8
$\therefore$ The value of 5$P_1$– $P_2$ is 7.8.
Hence, the correct answer is 7.8.
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