The Wentworth Company manufactures modular furniture for the home and uses a monthly variance system to control costs of the manufacturing departments. Edward Collins is the supervisor of the Assembly Department and is reviewing the monthly variance analysis for November, which showed a significant cost overrun (i.e., negative cost variance). Collins has gathered the following information to assist him in deciding whether or not to investigate the unfavorable cost variance for the Assembly Department:
Estimated cost (I) to investigate the variance $4,000
Estimated probability that the Assembly Department is operating properly, that is, the probability that the observed variance is a random event = (1 − p) = 9%
If the Assembly Department is operating out of control (i.e., improperly):
Estimated cost (C) to correct the process = $8,000
Estimated loss (L) if the observed variance is the result of a nonrandom cause but the company fails to investigate = $40,000
Required:
Collins is uncertain about the probability estimate of 90% for proper operation of the Assembly Department. Determine the probability estimate (to three (3) decimal places, for example, 0.04691 = 0.047) that would cause Collins to be indifferent between the two possible managerial actions: investigate or don't investigate the variance.

Question

The Wentworth Company manufactures modular furniture for the home and uses a monthly variance system to control costs of the manufacturing departments. Edward Collins is the supervisor of the Assembly Department and is reviewing the monthly variance analysis for November, which showed a significant cost overrun (i.e., negative cost variance). Collins has gathered the following information to assist him in deciding whether or not to investigate the unfavorable cost variance for the Assembly Department:
Estimated cost (I) to investigate the variance $4,000
Estimated probability that the Assembly Department is operating properly, that is, the probability that the observed variance is a random event = (1 − p) = 9%
If the Assembly Department is operating out of control (i.e., improperly): 
Estimated cost (C) to correct the process = $8,000
Estimated loss (L) if the observed variance is the result of a nonrandom cause but the company fails to investigate = $40,000
Required:
Collins is uncertain about the probability estimate of 90% for proper operation of the Assembly Department. Determine the probability estimate (to three (3) decimal places, for example, 0.04691 = 0.047) that would cause Collins to be indifferent between the two possible managerial actions: investigate or don't investigate the variance.

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The Answer of The Wentworth Company manufactures modular furniture for the home and uses a monthly variance system to control costs of the manufacturing departments. Edward Collins is the supervisor of the Assembly Department and is reviewing the monthly variance analysis for November, which showed a significant cost overrun (i.e., negative cost variance). Collins has gathered the following information to assist him in deciding whether or not to investigate the unfavorable cost variance for the Assembly Department:
Estimated cost (I) to investigate the variance $4,000
Estimated probability that the Assembly Department is operating properly, that is, the probability that the observed variance is a random event = (1 − p) = 9%
If the Assembly Department is operating out of control (i.e., improperly): 
Estimated cost (C) to correct the process = $8,000
Estimated loss (L) if the observed variance is the result of a nonrandom cause but the company fails to investigate = $40,000
Required:
Collins is uncertain about the probability estimate of 90% for proper operation of the Assembly Department. Determine the probability estimate (to three (3) decimal places, for example, 0.04691 = 0.047) that would cause Collins to be indifferent between the two possible managerial actions: investigate or don't investigate the variance.

The Wentworth Company Manufactures Modular Furniture for the Home and Uses