Question

1. in a study of 200 customers, the average spending was $150 with a standard deviation of $25. if most customers spent between $50 and $300, is this data consistent?

a. no, the data is inconsistent
b. yes, but the standard deviation is too large
c. yes, the data is consistent
d. theres not enough information

Explanation:

Step1: Calculate lower - bound z - score

The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $x = 50$, $\mu=150$, and $\sigma = 25$, we have $z_1=\frac{50 - 150}{25}=\frac{- 100}{25}=-4$.

Step2: Calculate upper - bound z - score

For $x = 300$, $\mu = 150$, and $\sigma=25$, we have $z_2=\frac{300 - 150}{25}=\frac{150}{25}=6$.

Step3: Analyze the z - scores

In a normal distribution, almost all (about 99.7%) of the data lies within 3 standard deviations of the mean ($z=-3$ to $z = 3$). A large portion of data lying between $z=-4$ and $z = 6$ is not typical for a normal - distributed data set. So the data is inconsistent.

Answer:

a. No, the data is inconsistent