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Two companies, A and B, drill wells in a rural area. Company A charges a flat fee of 3681 dollars to drill a well regardless of its depth. Company B charges 1168 dollars plus 10 dollars per foot to drill a well. The depths of wells drilled in this area have a normal distribution with a mean of 260 feet and a standard deviation of 40 feet. Find the probability that Company B would charge more than Company A to drill a well.

Respuesta :

Answer:

Mean costing =  $3,768

Step-by-step explanation:

Given:

Mean A(x) = 260

Rate = $10 per feet

Fixed charge = $1,168

Computation:

Assume;

depth = x ft

So,

Cost of company B = 10x + 1,168

So,

Mean costing = 10A(x) + 1,168

Mean costing =  10(260) + 1,168

Mean costing =  2,600 + 1,168

Mean costing =  $3,768

fichoh

Using the normal probability distribution concept, the probability that Company B would charge more than Company A to drill a well is 0.4146

Company A :

  • Cost = 3681 - - - - (1)

Company B :

  • Cost = 1168 + 10x - - - - (2)

Equating the cost ;

3681 = 1168 + 10x

3681 - 1168 = 10x

2513 = 10x

x = 251.3

Company B will charge more than Company A when depth exceeds 251.3 feets

Using the Z - score relation :

  • Z = (x - mean) / standard deviation

P(X > 251.3) = (251.3 - 260) / 40

P(X > 251.3) = -0.2175

Using the normal distribution table :

P(Z > -0.2157) = 1 - P(Z < -0.2157)

P(Z > 0.2157) = 1 - 0.58539

P(Z > 0.2157) = 0.4146

Hence, the probability that Company B would charge more than Company A to drill a well is 0.4146

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