Question

Using the information below, answer the next 6 questions: Yoonie is a personnel manager in a large corporation. Each month she must review the employees in her department. From past experience, she has found that the reviews take her approximately four hours each to do with a standard deviation of 1.2 hours. (1) What is the mean time to complete one review? QUESTION 2 (2) How long on average does it takes to complete two reviews? QUESTION 3 (3) What is the probability that one review will take Yoonie from 3.5 to 4.25 hours? (Round to 3 decimal places) QUESTION 4 What is the probability that one review will take Yoonie from less than 2.8 hours? (Round to 2 decimal places)

Answer 1

Slution: 1 mean time (1) taken to complete I review = 4 hours. 2) It takes it e = 8 hours to complete two reviews on an average. 3) This is normal distribution question with Mean (1) = 4. standard deviation (0) = 1.2 since we know that x-e Zgcone = x1 = 3-5 X2 = 4.25 P(3.5< X <4.25) = ? The Z-score at x = 3.5 is, 3.5 - 4.0 ZE12 2,-0.4167 The 2-score at x = 3.5 is 2- 4.25 -4.0 Zl= 0.2083 This implies that p(3.5< X < 4.25) = P(-0-4167 22 20-2083) EP (240-2083) - P(Z -0.4161) P (3-5 < x < 4.25) 20-5825026341772108 = 0.33844 892718314723 P (3-5 < X < 4.25) = 0.244.

4) 2=2.8 POXC2.8) = ? at x = 4.8 The Z-score is z. 2.8-4.0.3-1.0. Z : 1.2 This implies that P(x<&.8) = P(Z <-)0) = 0.1586 0.159 5) X = 6.4 P(xa > 6.4) = ? The z-score at x=6.4 is 2 6.4 - 4.0. =2.0 1.2 'This implies that p(2>6-4)= P(Z > 2.0)=1 -0.9772498680518208 P(x>6-4) = 0.0228 0.023. Ps: you have to reten z-score table to find probabilities. the final 6) P(x>6.41x>5-2) = P(Z>2)/P(251) = 0.025 0.16 - 0.156