The chickens at Colonel Thompson's Ranch have a mean weight of 1850g, with a standard deviation of 150g

# The chickens at Colonel Thompson's Ranch have a mean weight of 1850g, with a standard deviation of 150g

215 points

The chickens at Colonel Thompson's Ranch have a mean weight of 1850 g, with a standard deviation of 150 g. The weights of the chickens are closely approximated by a normal curve. Find the percent of all chickens having weights between 1606 g and 2288 g.

The chickens
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S
9.9k points

Our goal is to find all chickens having weights between 1606g and 2288g. To do this we start by finding the z-scores for the separate weights with $\mu = 1850$, and $\sigma = 150$. The equation for the z-score is,

$$z = \frac{x-\mu}{\sigma}$$

for the first weight of 1606g I get,

$$z = \frac{1606-1850}{150}\approx -1.63$$

and for the second weight of 2288g I get,

$$z = \frac{2288-1850}{150}\approx 2.92$$

so we are looking for the area under the normal curve for

this can be found by using the standard normal table. The area to the left of z = 2.92 is 0.9982. The area to the left of z = -1.63 is 0.0516. To get the area under the curve we take,

A = 0.9982 - 0.0516 = 0.9466

or 94.66% of all chickens have weights between 1606g and 2288g.

T
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