Question

a group of 150 students had heights that were roughly normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. about how many students will be taller than 70 inches? a 0 b 2 c 4 d 6 e 8

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 70$ (the value we are interested in), $\mu = 65$ (the mean), and $\sigma=2.5$ (the standard deviation). So $z=\frac{70 - 65}{2.5}=\frac{5}{2.5}=2$.

Step2: Find the proportion of data above the z - score

Using the standard normal distribution table, the proportion of data to the left of $z = 2$ is approximately $0.9772$. So the proportion of data to the right of $z = 2$ is $1-0.9772 = 0.0228$.

Step3: Calculate the number of students

We have a total of $n = 150$ students. The number of students taller than 70 inches is $n\times0.0228=150\times0.0228 = 3.42\approx4$.

Answer:

C. 4