STATISTICAL QUESTIONS

Statistical Questions



Math 160 Chapter 6 Quiz _________________________________

For each of the following problems, make sure you that you show your work. No credit will be given if no work or explanation is given for the problem. If using the TI-83 calculator, record what you are typing into the calculator to get your answer. For example, normal cdf(-2, 6, 1, 3). A picture using the normal curve may be helpful on these problems. No 2 quiz papers should be the same. Any questionable papers will not be graded and a Zero will be given.

1.) The time that it takes a randomly selected employee to perform a certain task is approximately normally distributed with a mean value of 123 seconds and a standard deviation of 17 seconds. The 15% that complete the task the fastest earn points on their job evaluation. What time qualify for this? State answer to 2 decimal places

(Hint: Draw a picture!!)

Only 15 % of them can do it faster than the others, which means that the rest of the 85% of the sample size is unable to be on the benchmark of being the fastest one. Therefore, in this case.

P (z>z*) = 0.85 = Z* < -2.17

Hence: (X-123)/17 < -2.17

After solving the answer would be: 86.11 seconds and below will qualify for it.

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2.) Express Courier Service has found that the delivery time for packages is normally distributed with mean 31 hours and a standard deviation of 4.75 hours.

a.) For a package selected at random, what is the probability that it will be delivered in 28 hours or less? (4 decimals)

The test value is taken as 28 hours, with the mean of 31 hours and standard deviation of 4.75 hours.

(X-Mean) / S.D = Z value

(28-31) / 4.75 = - 0.6315

Now see the probability ...