An experiment is designed to test whether operator A or operator B gets the job of operating a new machine. Each operator is timed on 75 independent trials involving the performance of a certain task on the machine. If the sample means for the 75 trials differ by more than 5 seconds, the operator with the smaller mean gets the job. Otherwise, the experiment is considered to end in a tie. Suppose the standard deviations of times for both operators are assumed to be 2 seconds. What is the probability that operator A gets the job even though both operators have equal ability

The probability that operator A gets the job even though both operators have equal ability is 0.0001.

Step-by-step explanation:

We are given that an experiment is designed to test whether operator A or operator B gets the job of operating a new machine. If the sample means for the 75 trials differ by more than 5 seconds, the operator with the smaller mean gets the job.

Suppose the standard deviations of times for both operators are assumed to be 2 seconds.

The z score probability distribution for the two-sample normal distribution is given by;

                   Z  =    ~ N(0,1)

where, = sample mean for operator A

= sample mean for operator B

= standard deviations of times for operator A = 2 seconds

= standard deviations of times for operator B = 2 seconds

= sample of independent trials for both operators = 75

Now, the probability that operator A gets the job even though both operators have equal ability is given by = P( > 5 seconds)

    P( > 5 sec) = P( > )

                                    = P(Z > 15.31) = 1 - P(Z 15.31)

                                                          = 1 - 0.9999 = 0.0001

As in the z table, the highest critical value for x is given for x = 4.40 so we will take this value's probability area for x = 15.31.

2,600 divided by 80 = 32.5

step-by-step explanation:

step-by-step explanation:

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