in the balcony of a theatre there are 420 seats. the number of seats in each row is 14 more than the number of rows. find the nu
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Answer:
a) P(X>np+3=0.017
b) P(x>1)=0.190
c) P(Y>1)=0.651
Step-by-step explanation:
This a binomial experiment where success is denoted by parts that need rework.
X ∼ B(n, p); n = 20; p = 0.01
The expected value of X is: E(X) = np =20×0.01= 0.2
The variance is: Var(X) = np(1 − p) = 0.2 × 0.99 = 0.198,
The standard deviation SD(X)= ≈ 0.445
a) P(X>np+3=P(X>0.2+3×0.445)=P(X>1.535)=P(X≥2)
Probability function is given by:
P(X≥2)=1-P(X<2)=1-P(X=1)-P(X=0)= 1 - -
P(X≥2)=1-0.165-0.818=0.017
b) p=0.04
P(x>1)=P(x≥2)= 1 - P(x=1) - P(x=0)= 1 - -
P(x>1)= 1 - 0.368 - 0.442=0.190
c) In this case we consider p=0.19 (Probability that X exceeds 1)
In this experiment Y is the number of hours and n= 5 hours.
Then, we check the probability in each hour:
P(Y>1)=1- P(Y=0)
P(Y=0)==0.349
P(Y>1)=1-0.349=0.651
The congruence theorem that can be used is: B. ASA
<h3>What is the ASA Congruence Theorem?</h3>If we have two triangles that have two pairs of corresponding congruent angles (e.g. ∠LGH ≅ ∠HKJ and ∠LHG ≅ ∠KHJ), and a pair of corresponding congruent sides (e.g. GH ≅ HK), the triangles are said to be congruent triangles by the ASA congruence theorem.
Therefore, triangles GHL and KHL in the image given are congruent triangles by the ASA congruence theorem.
Learn more about the ASA congruence theorem on:
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