Question

researchers observed the weights of a certain bird species in a habitat. the chart below indicates that the recorded weights follow a normal distribution with mean 160 g and standard deviation 10 g. approximately what percentage of the bird population weighs between 140 and 170 grams? a. 68% b. 95% c. 82% d. 60%

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set.
For $x = 140$, $z_1=\frac{140 - 160}{10}=\frac{- 20}{10}=-2$.
For $x = 170$, $z_2=\frac{170 - 160}{10}=\frac{10}{10}=1$.

Step2: Use the standard normal distribution table

The standard - normal distribution table gives the cumulative probability.
The cumulative probability for $z=-2$ is approximately $0.0228$.
The cumulative probability for $z = 1$ is approximately $0.8413$.

Step3: Find the probability between the two z - scores

$P(-2

Answer:

C. 82%