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: Recall normal - distribution property

In a normal distribution, values within 2 standard deviations of the mean are in the interval \(\mu - 2\sigma\leq x\leq\mu + 2\sigma\). From the graph, the mean \(\mu = 10\) and assume the standard - deviation \(\sigma = 0.5\). The interval is \(10-2\times0.5\leq x\leq10 + 2\times0.5\), which simplifies to \(9\leq x\leq11\).

Step2: Check each option

Check if each weight is in the interval \([9,11]\).

• For \(8.4\) lbs: \(8.4<9\), so it is not in the interval.
• For \(8.9\) lbs: \(8.9<9\), so it is not in the interval.
• For \(9.5\) lbs: \(9\leq9.5\leq11\), so it is in the interval.
• For \(10.4\) lbs: \(9\leq10.4\leq11\), so it is in the interval.
• For \(10.9\) lbs: \(9\leq10.9\leq11\), so it is in the interval.

Answer:

9.5 lbs, 10.4 lbs, 10.9 lbs