Question

the graph represents the normal distribution of recorded weights, in pounds, of cats at a veterinary clinic. weights of cats (lbs) which weights are within 2 standard deviations of the mean? select three options. 8.4 lbs 8.9 lbs 9.5 lbs 10.4 lbs 10.9 lbs

Explanation:

Step1: Determine the mean and standard deviation

From the graph, the mean $\mu = 9.5$ and the standard deviation $\sigma=0.5$.

Step2: Calculate the range within 2 standard deviations

The lower bound is $\mu - 2\sigma=9.5 - 2\times0.5=9.5 - 1 = 8.5$.
The upper bound is $\mu + 2\sigma=9.5+2\times0.5=9.5 + 1=10.5$.

Step3: Check each option

• For $8.4$: $8.4<8.5$, not within the range.
• For $8.9$: $8.5<8.9<10.5$, within the range.
• For $9.5$: $8.5<9.5<10.5$, within the range.
• For $10.4$: $8.5<10.4<10.5$, within the range.
• For $10.9$: $10.9>10.5$, not within the range.

Answer:

8.9 lbs, 9.5 lbs, 10.4 lbs