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Sagot :
Answer: 0.2417
Step-by-step explanation:
- 10! / (10-5)!5! x 0.53^5 x 0).47^5
To solve the problem we must know Binomial distribution.
The probability that exactly half have some college education is 17.3425%.
Given to us
- The probability of a person having at least some college education = 63% = 0.63
To solve the problem we will use the Binomial distribution, therefore,
- The probability of a person having at least some college education, p = 63% = 0.63
- The probability of a person not having at least some college education, q = 37% = 0.37
- Number of people selected for college education (Sample Size) = 10
Using the formula for Binomial Distribution,
We want the probability that exactly half have some college education, therefore, x = 5
[tex]P(x) = ^nC_x\ p^x\ q^{(n-x)}[/tex]
Substitute the values we get,
[tex]P(5) = ^{10}C_5\ (0.63)^{5}\ (0.37)^{(10-5)}\\\\P(5) = ^{10}C_5\ (0.63)^{5}\ (0.37)^{5}\\\\P(5) = 0.173425 = 17.3425\%[/tex]
Hence, the probability that exactly half have some college education is 17.3425%.
Learn more about Binomial distribution:
https://brainly.com/question/12734585
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