Question

a researcher is studying a group of field mice. the distribution of the weight of field mice is approximately normal with mean 25 grams and standard deviation 4 grams. which of the following is closest to the proportion of field mice with a weight greater than 33 grams?
a 0.023
b 0.046
c 0.954
d 0.977
e 1.000

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 33$ grams (the value of interest), $\mu = 25$ grams (the mean), and $\sigma = 4$ grams (the standard deviation). So, $z=\frac{33 - 25}{4}=\frac{8}{4}=2$.

Step2: Use the standard normal distribution table

The standard - normal distribution table gives the cumulative probability $P(Z\leq z)$. For $z = 2$, from the standard - normal table, $P(Z\leq2)=0.9772$.

Step3: Find the probability of $Z>2$

We know that $P(Z > z)=1 - P(Z\leq z)$. So, $P(Z>2)=1 - 0.9772 = 0.0228\approx0.023$.

Answer:

A. 0.023