SOLUTION: Use the following information to answer the following four questions: The error in taking various measurements of a rod is normally distributed with mean 17 in and standard deviati

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Question 1119558: Use the following information to answer the following four questions: The error in taking various measurements of a rod is normally distributed with mean 17 in and standard deviation 3.1 in.
27. What is the probability that a randomly selected measurement will be between 15 in and 19 in?
(a) 0.5123
(b) 0.4811
(c) 0.3956
(d) 0.2997
(e)
28. What is the probability that a randomly selected measurement will be less than 22 in?
(a) 0.9466
(b) 0.8675
(c) 0.7765
(d) 0.6875

29. What is the probability that a randomly selected measurement will be greater than 14.3 in?
(a) 0.9697
(b) 0.9090
(c) 0.8081
(d) 0.7885

30. A randomly selected measurement was found to be in the top 5%. What was its value?
(a) 24.08
(b) 23.07
(c) 22.09
(d) 21.06
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
questions like these can be answered very easily using the david m. lane normal distribution calculator.

the results of the use of that calculator in answering your questions are shown below:

27. What is the probability that a randomly selected measurement will be between 15 in and 19 in?
(a) 0.5123
(b) 0.4811
(c) 0.3956
(d) 0.2997
(e)

answer is selection b.

$$$

28. What is the probability that a randomly selected measurement will be less than 22 in?
(a) 0.9466
(b) 0.8675
(c) 0.7765
(d) 0.6875

answer is selection a.

$$$

29. What is the probability that a randomly selected measurement will be greater than 14.3 in?
(a) 0.9697
(b) 0.9090
(c) 0.8081
(d) 0.7885

answer is selection c.

$$$

30. A randomly selected measurement was found to be in the top 5%. What was its value?
(a) 24.08
(b) 23.07
(c) 22.09
(d) 21.06

answer is selection c.

$$$

this calculator can be found at http://davidmlane.com/hyperstat/z_table.html

use of a calculator such as this is doing it the easy way.
you don't have to convert to z-scores and you don't have to look up values in the z-score table and you don't have to interpolate when the area to the left of a z-score is not exactly as the areas found in the z-score tables.

the answers i got are very close to the correct answers, but they appear to be off by a digit.

i checked with the TI-84 Plus that can do the same calculations easily and found that your selections are the ones that are off.

it appears that they truncated to 4 decimal digits rather than rounding to 4 decimal digits.

for example, the answer i got for the first problem is .48117 which rounds to .4812.

the answer i got for the second problem was consistent with the selection, therefore no discrepancy there.

the answer i got for the third problem was consistent with the selection, therefore no discrepancy there.

the answer i got for the fourth problem was 22.099 which rounds to 22.1.
the selection said 22.09 so it appears they truncated rather than rounded there as well.

regardless, the answers i got were still closer to those selections than any of the other selections so it was reasonable to assume those selections were the ones they were looking for.