Question

In: Statistics and Probability

A manager at a local manufacturing company has been monitoring the output of one of the...

A manager at a local manufacturing company has been monitoring the output of one of the machines used to manufacture chromium shells. Past data indicate that if the machine is functioning properly, the length of the shells produced by this machine can be modeled as being normally distributed with a mean of 118 centimeters and a standard deviation of 4.3 centimeters. Suppose 10 shells produced by this machine are randomly selected. What is the probability that the average length of these 10 shells will be between 116 and 120 centimeters when the machine is operating "properly?"

Expert Solution

Given:

Given,

Mean, = 118

Standard deviation, = 4.3

n = 10

X ~ Normal (=118, ^2=4.3^2)

The probability that the average length of these 10 shells will be between 116 and 120 centimeters when the machine is operating properly :

P(116 < < 120) = P ((116-)//√n < (X-)//√n < (120-)//√n)

= P((116-118)/4.3/√10 < Z < (120-118)/4.3/√10)

= P(-1.47 < Z < 1.47)

= P(Z< 1.47) - P(Z< -1.47)

= 0.9292 - 0.0708

= 0.8584

The probability that the average length of these 10 shells will be between 116 and 120 centimeters when the machine is operating properly is 0.8584

orchestra answered 1 year ago

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