7. Elephants are the mammals with the longest gestation period. One species of elephant has a mean gestation period of 635 days and a standard deviation of 63 days. Assume that a random sample of 42 elephants was taken.What is the probability that sample mean gestation period is above 650 days? (round your answer to four decimal space)- a. 0.9332- b. 0.0618- c. 0.9382- d. 0.0668

Let X represents the gestation period. Given that, X~ N(635, 63) μ= 635, σ= 63 Sample size is n= 42Then mean of gestation period = 635 and standard deviation = σ/sqrt(n) = 63/sqrt(42) =9.7211 x̄~ N(635,9.7211)Z score for x̄ is given by, Z score= (x̄-ux̄)/σx̄ P(x̄>650)=P(z>(650-635)/9.7211) = P(z>1.54) =1-P(z<1.54) from z score table, = 1-0.9382 =0.0618 option (b) is correct.