A survey of pet owners found that on average, they spend \( \$ 1,225 \) annually per pet, with a standard deviation of \( \$ 275 \), Between which two amounts would you expect \( 95 \% \) of the survey's respondents to spend annually per pet if the sample is approximately normal and comes from a normally distributed population? \( \$ 675 \) and \( \$ 1,500 \) \( \$ 675 \) and \( \$ 1,775 \) \( \$ 950 \) and \( \$ 1,500 \) \( \$ 950 \) and \( \$ 1,775 \)

To find the range where approximately 95% of respondents fall in a normally distributed population, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, approximately 95% of the data lies within two standard deviations of the mean. In this case, the mean annual spending is \( \$ 1,225 \) and the standard deviation is \( \$ 275 \). So, we calculate: 1. Two standard deviations below the mean: \(\$ 1,225 - 2 \times \$ 275 = \$ 1,225 - \$ 550 = \$ 675\) 2. Two standard deviations above the mean: \(\$ 1,225 + 2 \times \$ 275 = \$ 1,225 + \$ 550 = \$ 1,775\) Therefore, you would expect that 95% of the survey's respondents spend between \( \$ 675 \) and \( \$ 1,775 \). So the correct answer is: \( \$ 675 \) and \( \$ 1,775 \)