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Nuts and Berries: Combined Standard Deviation

APSTAT-IFEZLJ

Nuts and Berries is an online company that sells different types of nut butters (like peanut butter and almond butter) and different types of jams (like raspberry jam and grape jam). Jams are sold in $8$ oz quantities and nut butters are sold in $12$ oz quantities.

Of course, not every jar is filled with precisely the advertised weight. When determining shipping costs, there is also the weight of the jar to consider.

If the mean weight of one jar of jam (of any variety) is $8.6$ oz with a standard deviation of $0.17$ oz, and the average weight of a jar of nut butter (of any variety) is $12.7$ oz with a standard deviation of $0.23$ oz, what is the standard deviation of the weight of an order consisting of $3$ jars of jam and one jar of nut butter?

A

$0.098\text{ oz}$

B

$0.17\text{ oz}$

C

$0.23\text{ oz}$

D

$0.74\text{ oz}$

E

$0.374\text{ oz}$