Question

The weight, in pounds, of a certain type of adult squirrel is normally distributed with a mean of 4.1 pounds and a standard deviation of 0.5 pounds. What percentage of squirrels have a weight between 3 and 5 pounds?

Answer 1

Answer:

95.02% of squirrels have a weight between 3 and 5 pounds.

Step-by-step explanation:

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.1 pounds

Standard Deviation, σ = 0.5 pounds

We are given that the distribution of weight is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(weight between 3 and 5 pounds)

$P(3 \leq x \leq 5) = P(\displaystyle\frac{3 - 4.1}{0.5} \leq z \leq \displaystyle\frac{5-4.1}{0.5}) = P(-2.2 \leq z \leq 1.8)\\\\= P(z \leq 1.8) - P(z < -2.2)\\= 0.9641- 0.0139 = 0.9502= 95.02\%$

$P(3 \leq x \leq 5) = 95.02\%$

95.02% of squirrels have a weight between 3 and 5 pounds.