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: Identify mean and standard - deviation range concept

In a normal distribution, values within 2 standard deviations of the mean are in the range $\mu - 2\sigma$ to $\mu+2\sigma$. From the graph, assume the mean $\mu = 9.5$ and standard - deviation $\sigma = 0.5$. The range is $9.5-2\times0.5=8.5$ to $9.5 + 2\times0.5 = 10.5$.

Step2: Check each option

Check if each weight is within the range $[8.5,10.5]$.

• For 8.4 lbs: $8.4<8.5$, not in the range.
• For 8.9 lbs: $8.5\leq8.9\leq10.5$, in the range.
• For 9.5 lbs: $8.5\leq9.5\leq10.5$, in the range.
• For 10.4 lbs: $8.5\leq10.4\leq10.5$, in the range.
• For 10.9 lbs: $10.9>10.5$, not in the range.

Answer:

8.9 lbs, 9.5 lbs, 10.4 lbs