A sample of 10 packs of a brand of chewing gum was taken. Each pack was weighed and their weights, in grams, are shown.

Question

A sample of 10 packs of a brand of chewing gum was
taken. Each pack was weighed and their weights, in
grams, are shown.
What is the Z-score for the pack of gum weighing 43
grams?
01.13
43.0, 43.7, 49.6, 46.9, 47.6, 45.4, 51.2, 48.0, 40.5, 49.1
11.05
01.05
01.13

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Edana Edana 5 months 2021-08-16T04:36:05+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-08-16T04:37:40+00:00

    Answer:

    The z-score is approximately -1.05

    Step-by-step explanation:

    The given data of the weights of the packs of chewing gum are;

    43.0, 43.7, 49.6, 46.9, 47.6, 45.4, 51.2, 48.0, 40.5, and 49.1

    The number of chewing gums in the sample, n = 10

    The sum of the weights of the chewing gums is therefore;

    43.0+43.7+49.6+46.9+47.6+45.4+51.2+48.0+40.5+49.1 = 465

    The average weight is given as follows;

    The average weight of the chewing gums = (The sum of the weights of the chewing gums)/(The number chewing gums)

    The average weight, μ, of the chewing gums = (465)/(10) = 46.5

    The standard deviation, σ, is given by the formula;

    \sigma =\sqrt{\dfrac{\sum (x_{i} - \mu )^{2}}{n-1}}

    Where;

    x_i = Each individual chewing gum weight values

    With the standard deviation formula in Excel, we have;

    σ ≈ 3.323 grams

    The z-score, z, is given by the following formula;

    Z=\dfrac{x-\mu }{\sigma }

    Therefore, the z-score of 43 is given as follows;

    Z=\dfrac{43-46.5 }{3.323 } \approx -1.05

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