Question

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 surveys 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

Explanation:

Step1: Recall the empirical rule for normal distribution

For a normal distribution, about 95% of the data lies within 2 standard - deviations of the mean.

Step2: Calculate the lower bound

The mean $\mu = 1225$ and the standard deviation $\sigma=275$. The lower bound is $\mu - 2\sigma=1225-2\times275 = 1225 - 550=675$.

Step3: Calculate the upper bound

The upper bound is $\mu + 2\sigma=1225 + 2\times275=1225 + 550 = 1775$.

Answer:

$675$ and $1775$, so the answer is B. $675$ and $1775$