Question

Statistics

Posted 3 months ago

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Jacqueline works as a quality control expert at a factory that packages different chocolates in variety packs. She selected a random container to see how well the 220 chocolates inside matched the advertised distribution. The table below shows the advertised distribution and the observed counts for each type of chocolate in the container she selected.
\begin{tabular}{lrrrr}
Type of chocolate & Dark & Milk & Salted caramel & White \\
\hline Advertised & $40 \%$ & $30 \%$ & $20 \%$ & $10 \%$ \\
\# of chocolates observed & 81 & 75 & 48 & 16
\end{tabular}
Jacqueline wants to perform a $\chi^{2}$ goodness-of-fit test to determine if these results suggest that the actual distribution of chocolates doesn't match the advertised distribution.
What is the expected count of salted caramel chocolates in Jacqueline's sample?
You may round your answer to the nearest hundredth.
Expected: $\square$
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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

To find the expected count of salted caramel chocolates, we first need to determine the total number of chocolates in the sample, which is given as 220

step 2

The advertised percentage for salted caramel chocolates is 20%. To find the expected count, we multiply the total number of chocolates by the advertised percentage:
$\text{Expected count} = 220 \times 0.20$

step 3

Performing the multiplication:
$\text{Expected count} = 220 \times 0.20 = 44$

Answer

The expected count of salted caramel chocolates is 44.

Key Concept

Expected count calculation

Explanation

The expected count is found by multiplying the total number of chocolates by the advertised percentage for the specific type of chocolate.

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