Question

1. a sample of 40 students has a mean score of 80 and a standard deviation of 10. if most values fall between 70 and 90, is this data consistent?

a. no, the data is inconsistent
b. yes, the data is consistent
c. no, the sample size is too small
d. yes, the standard deviation is too large

Explanation:

Step1: Recall the empirical rule for normal - distribution

In a normal distribution, about 95% of the data lies within 2 standard deviations of the mean. The formula for the range within $k$ standard deviations of the mean is $\mu\pm k\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Calculate the range within 2 standard deviations of the mean

Given $\mu = 80$ and $\sigma=10$, the range within 2 standard deviations is $\mu - 2\sigma$ to $\mu + 2\sigma$.
$\mu-2\sigma=80 - 2\times10=60$
$\mu + 2\sigma=80+2\times10 = 100$.
If most values (about 95% in a normal - distribution) are expected to be within 2 standard deviations of the mean, and we are given that most values fall between 70 and 90. Since 70 and 90 also fall within the range of 60 - 100 (the 2 - standard - deviation range), the data is consistent.

Answer:

b. Yes, the data is consistent