Download Hints for completion

Hints for completion
Excel has a selection of functions relating to the normal distribution and confidence intervals. For
normal distribution questions, in a similar manner to using the printed tables, a little thought has to go
into the manipulation of the functions to reach the desired outcome. The different commands and
examples of how these can be manipulated are given below.
Please note that due to the greater accuracy of Excel some answers gained by use of the tables may
differ from those found on the spreadsheet.
Standard normal distribution i.e., Z ~ N(0, 12)
=NORMSDIST(Z): returns the probability for P(Z <= z)
i.e., the area below any (positive or negative) value of z.
Examples
To find P(Z < 1.68) the function used is =NORMSDIST(1.68).
To find an area above z remember that the area under the whole curve is 1 and therefore the area above a
value of z is (1 – Area below z).
So to find P(Z > 2.1) the formula to enter is =1–NORMSDIST(2.1).
=NORMSINV(p): gives the Z value found when using tables backwards
Example
To find the value ? such that P(X< ?) = 0.1 the function is =NORMSINV(0.1)
i.e., the z value corresponding to the bottom 10% of the curve.
=STANDARDIZE(Value, Mean, Std Dev.): converts values from any normal distribution
to the standard normal distribution i.e., x  z
Example
If X is normally distributed with a mean of 50 and a standard deviation of 10, find the value of z when x
= 45.
The function required is = STANDARDIZE(45,50,10).
Normal distributions i.e., X ~ N(, 2)
Calculates (X <=x)
Calculates P(X) = x
(rarely used)
=NORMDIST(Value, Mean, Std Dev., Cumulative: TRUE or FALSE)
Example
The lengths of printer cable from a production line are normally distributed with a mean of 2 m and a
standard deviation of 0.05 m. Find the probability that a length of printer cable picked at random is less
than 1.9 m long.
The required function is =NORMDIST(1.9,2,0.05,TRUE).
Watch out! There is very little difference between the function wording NORMDIST and NORMSDIST
(standard normal) and this can cause frustration when errors occur.
=NORMINV(area, mean, Std Dev.): this function is used for problems where the
probability is known and the X value for a normal distribution is required
Example
A group of students scored an average of 57 on an exam with a standard deviation of 9. If the bottom
10% of the group failed what was the pass mark for the exam?
The function required is =NORMINV(0.1,57,9).
Confidence intervals for samples
=CONFIDENCE(interval proportion, standard deviation, sample size)
Note this formula represents the range either side of the sample mean. It does not give the final
confidence interval range.
Example
If the sample mean is 45 based on a sample of 50 items and the standard deviation is 4, find a 95%
confidence interval for the true mean (μ).
The required upper and lower limits of the interval would be given by
= 45 – CONFIDENCE(0.05,4,50) (lower limit)
= 45 + CONFIDENCE(0.05,4,50) (upper limit)
Here 0.05 represents the area in both tails i.e., 5%.
Population confidence intervals
In this case there is no specific function and the lower and upper limits are simply constructed from first
principles.