Chapter 20, Problem 1E

(a)

To determine

Find the standard deviations of the mean weight of the salmon in each type of shipment.

Answer to Problem 1E

The standard deviations are 1 pound, 0.5 pound and 0.2 pounds for 4 salmons, 16 salmons and 100 salmons respectively.

Explanation of Solution

Given info:

A food company sells King Salmon to customers. The mean weight of these salmon is 35 pounds and standard deviation is 2 pounds. They delivered three different restaurants in boxes with 4 salmon, in cartons 16 salmon and in pallets 100 salmon respectively.

Calculation:

Standard deviation:

For shipment of 4 salmon the standard deviation is,

$SD=\frac{\sigma }{\sqrt{n}}=\frac{2}{\sqrt{4}}=1$

For shipment of 16 salmon the standard deviation is,

$SD=\frac{\sigma }{\sqrt{n}}=\frac{2}{\sqrt{16}}=0.5$

For shipment of 100 salmon the standard deviation is,

$SD=\frac{\sigma }{\sqrt{n}}=\frac{2}{\sqrt{100}}=0.2$

Thus, the standard deviations are 1 pound, 0.5 pound and 0.2 pounds for 4 salmons, 16 salmons and 100 salmons respectively.

(b)

To determine

Explain whether the distribution of shipping weights would be better characterized by a normal model for the boxes or pallets.

Explanation of Solution

Given info:

The distribution of the salmon weights turns out to be skewed to the high end.

Justification:

By the central limit theorem, it can be said that for large sample size the distribution of the population mean follows normal distribution.

If pallets contain large number of salmon than the boxes, then the distribution of shipping weights is better characterized by a Normal model for the pallets. Otherwise, it would not be good to characterize by a Normal model.