1)
The z-score shows the dispersion from the mean. It is computed using the following formula.
z-score =
Given x = 9, μ =10, and σ = 4. So,
z-score =
2)
The population standard deviation of 0, 4, and 5 is calculated as follows:
s.d =
Thus, we need to obtain the mean =

S.d =

3)
The minimum is the observation with the least value in a sample, and the maximum is the
largest number. Since the observations 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 are
arranged in ascending order, the first observation is the minimum and the last maximum.
Minimum = 1
Maximum = 233
To obtain the first quarter (25%) we multiply the number of observations (n = 13) by 25%.
= =0.25*13 = 3.25
Thus, the 4 th observation is the first quarter.

STATISTICS 3
First quarter = 3
The median is the observation at the center/middle (13/2 = 6.5 = 7 th observation)
Median = 13
Upper quartile = 0.75*13 = 9.95 = 10 th observation
Upper quartile = 89
Inter-quartile range =upper quartile – lower quartile

= 89 – 3
= 86

4)
A standard deviation of zero deduces that the data sample are not spread, which in other
words means that they are clumped around a single value (Taylor, 2015).
5)
It is expected that about 95% of the observations to lie between 2 standard deviations of the
mean.
6)
It is anticipated that about 98.8% of the observations to lie between 2.5 standard deviations of
the average.
7)
Normally distributed means that the population distribution has a bell-shaped density curve,
which can be described by its mean (average) and standard deviation . Furthermore, the

STATISTICS 4
density curve is symmetrical, clustered around the mean, and the standard deviation
determines the spread of the plot.
8)
P (x < 60000) = z () =
P (x < 60000) = 0.8413
Therefore, 84.13% of people have salaries of $60,000or less.
9)

P (x < 40000) = z () =

=
= 0.1587
Therefore, 15.87% of people have salaries of $40,000or less.

STATISTICS 5

References

Taylor, C. (2015). When Is the Standard Deviation Equal to Zero?