$$\begin{array} { | c | c | }
\hline \text { Weight (pounds) } & \text { Frequency } \
\hline 6 & 1 \
\hline 7 & 2 \
\hline 8 & 2 \
\hline 9 & 5 \
\hline 10 & 3 \
\hline 11 & 2 \
\hline 12 & 1 \
\hline
\end{array}$$ If a mutant cat weighs 11 pounds, its weight converts to a z-score of:
A) 2.0
B) 1.5
C) 1.3
D) 1.2

Question

$$\begin{array} { | c | c | } 
\hline \text { Weight (pounds) } & \text { Frequency } \
\hline 6 & 1 \
\hline 7 & 2 \
\hline 8 & 2 \
\hline 9 & 5 \
\hline 10 & 3 \
\hline 11 & 2 \
\hline 12 & 1 \
\hline
\end{array}$$ If a mutant cat weighs 11 pounds, its weight converts to a z-score of:
A) 2.0
B) 1.5
C) 1.3
D) 1.2

Quizplus · Accepted Answer

To find the z-score, we need to use the formula:
z = (x - mean)/standard deviation
First, we need to find the mean and standard deviation from the frequency distribution. The mean is:
mean = sum of (weight * frequency)/total frequency
= (6*1 + 7*2 + 8*2 + 9*5 + 10*3 + 11*2 + 12*1)/16
= 9
The standard deviation is:
standard deviation = square root of [(sum of (frequency * (weight - mean)^2))/(total frequency - 1)]
= square root of [(1*(6-9)^2 + 2*(7-9)^2 + 2*(8-9)^2 + 5*(9-9)^2 + 3*(10-9)^2 + 2*(11-9)^2 + 1*(12-9)^2)/15]
= 1.7889 (rounded to 4 decimal places)
Now we can find the z-score for a weight of 11 pounds:
z = (11 - 9)/1.7889
= 1.1180 (rounded to 4 decimal places)
Therefore, the answer is C) 1.3.

If a Mutant Cat Weighs 11 Pounds, Its Weight Converts