Question

Mary Bartel an Auditor for a large credit card company, knows that on average, the monthly balance ofany given customer is $ 112 and the standard deviation is $ 56. If Mary audits 50 randomly selected accounts,what is the probability that the sample average monthly balance is (i)below $ 100(ii)between $ 100and$ 130

Answer 1

Step-by-step explanation:

Given Mary Bartel an Auditor for a large credit card company, knows that on average, the monthly balance of any given customer is $ 112 and the standard deviation is $ 56. If Mary audits 50 randomly selected accounts, what is the probability that the sample average monthly balance is (i)below $ 100(ii)between $ 100 and$ 130

• So for P < 100 we have
• Let x be the monthly balance.
• So given μ = 112 and σ = 56
• So sample will be n = 50
• So Probability x bar < 100 will be
•      Z = x bar – μ / σ / √n
•         = 100 – 112 / 56 / √50
•         = - 12 / 7.92
•          = -1.51
• So P (x bar < 100)
•       = Prob (Z < 1.51)
•      = - 0.0643
• Now between $ 100 and $ 120 we get
•      Prob ($ 100 < x bar < $ 130)
•         Z1 = x1 bar – μ / σ / √n
•              = 100 – 112 /56 / √50
•               = - 12 / 7.92
•              = - 1.51
•          Z2 = x2 bar – μ / σ / √n
•              = 130 – 112 / 56 / √50
•               = 18 / 7.92
•               = 2.27
•            So Prob (- 1.51 < z < 2.27)
•                  = 0.4357 + 0.4884
•                  = 0.9241

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