Download Normal Calculations Practice

Normal Calculations Practice
Name________________________________
Show all work and use the 3 step process when applicable.
1. Suppose a data set is represented by a normal distribution with a mean of 125 and a standard deviation of 7.
(a) What data value is 2 standard deviations above the mean?
_________________
(b) What data value is 3 standard deviations below the mean?
_________________
(c) What data value is 1.5 standard deviations below the mean?
_________________
(d) What data value is 2.5 standard deviations above the mean?
_________________
(e) What data value is 1 5 of a standard deviation above the mean?
_________________
2. What are the z-scores for the data values in parts (a)-(e) of the previous question?
(a)
z = _____________________
(d)
z = _____________________
(b)
z = _____________________
(e)
z = _____________________
(c)
z = _____________________
3. In a normally distributed data set, find the value of the standard deviation if the following additional
information is given.
(a) The mean is 226.2 and the z-score for a data value of 230 is 0.2.
σ = ________________
(b) The mean is 9.8 and a z-score for the data value of 10.3 is 2.
σ = ________________
(c) The mean is 14.6 and the z-score for a data value of 5 is −0.3.
σ = ________________
4. Find the percentages of observations from the standard Normal distribution that are:
(a) less than -1.6
(b) greater than 0.53
(c) between -0.15 and 1.40
(d) within .75 standard deviations of the mean
5. A patient recently diagnosed with Alzheimer’s disease takes a cognitive abilities test and scores a 45. The mean
on this test is 52 and the standard deviation is 5. What is the patient’s percentile rank?
6. Suppose that a certain insect has a mean lifespan of 5.6 days with a standard deviation of 1.2 days. Assume that
the lifespan of this insect is approximately normally distributed.
(a) Calculate the percentage of insects with a life-span between 3.2 and 8 days.
(b) Calculate the percentage of insects with a life-span between 2.6 and 8.6 days.
(c) What percentage of insects will live longer than 3.32 days?
(d) What percentage of insects will live less than 6.56 days?
7. A fifth grader takes a standardized achievement test. The test results are approximately normal with a mean of
125 and a standard deviation of 15. If the child scored at the 93 percentile, what score did he make on the test?