A dart is to be thrown at a target. The probability the dart will hit the target (yes or no) on a single attempt is 0.20. Each throw is independent of the other throws. Let X be the number of attempts before the target is hit.
a. What type of distribution does X follow?
b. Compute the expected number of attempts needed before hitting the target?
c. What is the variance and standard deviation of the number of attempts needed before hitting the target?
d. What is the probability that it will take less than 5 throws before hitting the target?

a) X has geometric distribution with parameter 0.2

b) The expected number of attempts before hitting the target is 5

c) The variance is 20, the standard deviation is √20

d) The probability that less than 5 throws are needed before hitting the target is 0.5904.

Step-by-step explanation:

a) X has geometric distribution, with parameter p=0.2.

b) If X is geometric with parameter p, then its mean is 1/p and the variance is . With p = 0.2, the mean is 1/0.2 = 5. As a consecuence, the expected number of attempts before hitting the target is 5.

c) The variance with p = 0.2 is 0.8/0.2² = 20. The standard deviation is √20.

d) The probability that it takes less than 5 throws before hitting the target can be computed with the probability of the complementary event: the probability that the first 4 targets miss. That probability is 0.8⁴=0.4096. Therefore, the probability that it will take less than 5 throws before hitting the target is 1-0.4096 = 0.5904.

take the top number and divide it by a the bottom number

step-by-step explanation:

1/2 1 divied by 2 = .5

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights