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


Asked by 1 year ago
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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2 Answers

S
Answered by 1 year ago
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

Wolfram Alpha normal curve plot

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
Answered by 6 months ago
0 points

Oh Snap! This Answer is Locked

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

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