Respuesta :
The probability of getting at least 7 questions correct on this test is 0.08665%.
What is Binomial distribution?
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
The probability of getting an answer right is 1/5, while the probability of getting it wrong is 4/5. Therefore, the probability of getting at least 7 questions correct on this test is,
P(X≥7) = P(X=7) + P(X = 8) + P(X=9) + P(X = 10)
= ¹⁰C₇ (1/5)⁷ (4/5)³ + ¹⁰C₈ (1/5)⁸ (4/5)² + ¹⁰C₉ (1/5)⁹ (4/5)¹ + ¹⁰C₁₀(1/5)¹⁰(4/5)⁰
= 0.0007886 + 0.000073728+ 0.000004096 + 0.0000001024
= 0.0008665264
= 0.08665%
Hence, the probability of getting at least 7 questions correct on this test is 0.08665%.
Learn more about Binomial Distribution:
https://brainly.com/question/14565246
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