Final EXAM STA/MA 30 FALL 20L All questions carry equal weight of 7 points each

Question

Final EXAM STA/MA 30 FALL 20L All questions carry equal weight of 7 points each You may use the STA TTREK probability distribution ealedators. - Show work for full credi freight elevator can transport a maximum of 9950 pounds, Suppose a load of containing 49 boxes must be transported via the elevator. The weights of the independent and identically distributed random variables with common 5) A large cargo boxes are mean -205 pounds and standard denote the sum of the weights of the 49 boxes. deviation = 15 pounds. Let the random variable Sa The mean E(Sap/49) and the standard deviation [Var(S, 49))'2 are i) (a) 205 and 15/7 (b) 205 and 15/49 (c) 10045 and 15 (d) 10045 and 735 ii) The Central Limit Theorem states that the probability distribution of the average weight Sa9 /49 of the boxes is approximated by (a) Nu-205, 2-15/49) (b) N(H 10045, o 735) (c) N(-205, 2-225/49) (d) N(= 10045, d-225) ii) Pall 49 boxes can be safely loaded on to the elevator and transported) is approximtely (a) 0.637 (b) 0.432 (c) 0.393 (d) 0.183

Explanation / Answer

i) mean = 205 and
sd (Xbar) = 15/sqrt(49) = 15/7
a) is correct

ii) c) is correct

iii) P(S < 9950)
= P(Xbar < 9950/49)
=P(Z <(9950/49 - 205)/(15/7)))
=P(Z < -0.9047619)
= 0.18279

option D) is correct

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