Question

you work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. the manufacturer claims that the life - spans of the tires are normally distributed, with a mean of 40,000 miles and a standard deviation of 3500 miles. you test 16 tires and get the following life - spans. 47,341 40,426 27,908 34,457 32,241 39,052 42,528 36,365 25,392 30,739 34,330 38,029 33,043 37,079 37,699 43,495. choose the correct answer below. is it reasonable to assume that the life - spans are normally distributed? why? choose the correct answer below. (b) find the mean of your sample. the mean is (round to one decimal place as needed.)

Explanation:

Step1: Recall the formula for sample mean

The formula for the sample mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the individual data - points and $n$ is the number of data - points. Here, $n = 16$ and the data points are $x_1=47341,x_2 = 40426,\cdots,x_{16}=43495$.

Step2: Calculate the sum of the data points

$\sum_{i = 1}^{16}x_{i}=47341 + 40426+27908+34457+32241+39052+42528+36365+25392+30739+34330+38029+33043+37079+37699+43495=550022$.

Step3: Calculate the sample mean

$\bar{x}=\frac{\sum_{i = 1}^{16}x_{i}}{16}=\frac{550022}{16}=34376.4$.

Answer:

$34376.4$