1 One thousand employees are given a standard test to measur

1. One thousand employees are given a standard test to measure job performance. The top 10 are to be given trips to Hawaii and the bottom 30 scorers are to be given trips back to training school. Assuming that the distribution is normal, M = 65 and SD = 10, what score must one get to be given a trip to Hawaii?

2. One thousand employees are given a standard test to measure job performance. The top 10 are to be given trips to Hawaii and the bottom 30 scorers are to be given trips back to training school. Assuming that the distribution is normal, M = 65 and SD = 10, what score must one get to end up back in training school?

Solution

To get a trip to Hawaii, you have to be on the top 10, or 990 students must be lower than you. Thus, the left tailed area is 990/1000 = 0.99.

Thus, the corresponding z score to that is\\

z(0.99) = 2.326347874

Thus, as

x = u + z*sigma

Then

x = 88.26 [ANSWER]

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The left tailed area here is 30/1000 = 0.03. Thus, the z score for that is

z = -1.880793608

Thus, as

x = u + z*sigma

Then

x = 46.19 [ANSWER]