Answer:
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 = <u>0.0001</u>
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.