researchers observed the weights of a certain bird species in a habitat. the chart below indicates that the…
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%
Answer
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
$P(-2<Z<1)=P(Z < 1)-P(Z < - 2)=0.8413-0.0228 = 0.8185\approx82%$.
Answer:
C. 82%