Statistics: Random Sample of Packages
Thank you. At a nearby post office, the weight of packages mailed out has a mean of 3.22
pounds and a standard deviation of 1.06 pounds. Consider a random sample of 50 packages
mailed out from this post office in the last year. Find the probability that the average weight of
these packages exceeds 3.4 pounds. Clearly state the distribution of the sample mean and find the
probability. Is your answer exact or approximate?
Solution
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We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 3.4
u = mean = 3.22
n = sample size = 50
s = standard deviation = 1.06
Thus,
z = (x - u) * sqrt(n) / s = 1.200747364
Thus, using a table/technology, the right tailed area of this is
P(z > 1.200747364 ) = 0.114924608 [ANSWER]
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BY central limit theorem, the distribution of the means will be NORMALLY DISTRIBUTED.
This is an approximate, because we only have a limited sample size..
Summarise the behavioural differences between subcritical and superc.pdf
1. Summarise the behavioural differences between subcritical and supercritical flow. How do these
two types of flow behave differently?
Solution
Subcritical flow is deep, slow flow with a low energy state and has a Froude number less than
one (F<1).
Critical flow occurs when the Froude number equals one (F=1); there is a perfect balance
between the gravitational and inertial forces.
Supercritical flow is shallow, fast flow with a high energy state and has a Froude number greater
than one (F>1). The energy state of the river affects the potential for entrainment and erosion of
the channel boundary as well as affecting the extent to which downstream disturbances to
forward flow from boulders or built structures can be transmitted upstream.
When flow conditions are subcritical, disturbances in the flow can generate surface waves, and
because the downstream flow is so slow, those surface waves can travel in an upstream direction.
When flow conditions are supercritical, surface waves generated by downstream disturbances
cannot travel upstream; the forward flow of water carries the waves downstream.
