Math

QuestionFor the probability mass function f(x)=x155f(x)=\frac{x}{155} for x=10,11,,20x=10,11, \ldots, 20 Find F(15) (Write in the form of an integer or decimal)
Answer:

Studdy Solution
Calculate the cumulative probability F(15) F(15) by summing the probabilities from the PMF for x=10 x = 10 to x=15 x = 15 .
F(15)=x=1015f(x) F(15) = \sum_{x=10}^{15} f(x)
Calculate each probability:
f(10)=10155 f(10) = \frac{10}{155} f(11)=11155 f(11) = \frac{11}{155} f(12)=12155 f(12) = \frac{12}{155} f(13)=13155 f(13) = \frac{13}{155} f(14)=14155 f(14) = \frac{14}{155} f(15)=15155 f(15) = \frac{15}{155}
Sum these probabilities:
F(15)=10155+11155+12155+13155+14155+15155 F(15) = \frac{10}{155} + \frac{11}{155} + \frac{12}{155} + \frac{13}{155} + \frac{14}{155} + \frac{15}{155}
F(15)=10+11+12+13+14+15155 F(15) = \frac{10 + 11 + 12 + 13 + 14 + 15}{155}
Calculate the numerator:
10+11+12+13+14+15=75 10 + 11 + 12 + 13 + 14 + 15 = 75
Now, divide by 155:
F(15)=75155 F(15) = \frac{75}{155}
Simplify the fraction:
F(15)=1531 F(15) = \frac{15}{31}
Convert to decimal:
F(15)0.4839 F(15) \approx 0.4839
The value of F(15) F(15) is approximately:
0.4839 \boxed{0.4839}

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