Statistics Formulae ΣΑ Mean. με Σ Sample Variance = s. Some Probability Formulae P(AUB) = P(A) + P(B)- P(AOB) 1. PANB) ; P(B)>0 2. P(A B) = PB) 3. P(AnB) = P(A/ B)+ P(B) 4. P(AIB) = P(A) P(AnB) = P(A)...

solve the following questions, attached is the formulas as well

Extracted text: Statistics Formulae ΣΑ Mean. με Σ Sample Variance = s. Some Probability Formulae P(AUB) = P(A) + P(B)- P(AOB) 1. PANB) ; P(B)>0 2. P(A B) = PB) 3. P(AnB) = P(A/ B)+ P(B) 4. P(AIB) = P(A) P(AnB) = P(A) • P(B) 5. P(A) = PA/ B)B) + PA/B)P(P(B) 6. P(BI A)P(A) 8. P(A B) = PBI A)P(A) + PMBIA)PA) με ΕίX) Σα) 9. a =V(X) = E[(X - ']=E(x-' P(x) 10. a =V(X) = E(X) -[E(X)r 11. n! 12. P(x) = 13. = np: o = npq Plx) = 'e". 14. for x= 0,1,2,3. 15. P(x)=pqx-


Extracted text: Question #3 The weight of a modomby chosen grape of a giren vaiety may be taken to be a normal vaniable with mean 5g Find the standard deriation, in grams, giren that the probability that a randomly chosen grape weighs less than 3g is 0.123. Find the probability that a sadomly chosen gape weighs more than 9g Fre grapes ace chosen at sandom Find the puobabiley that at least rwo weigh les han () Using a suitable appuosimaion, fad the probability that, out of 100 zaadomly chosen grapes at least 3 weigh more than 9g