wolf has an average weight of 44 lbs. with a standard deviation of 3 lbs. what percent of wolves weigh under 40 lbs.?
To determine the percentage of wolves that weigh under 40 lbs, we need to calculate the z-score and find the corresponding percentile.
1. Calculate the z-score using the formula:
z = (x - μ) / σ
where x is the given weight (40 lbs), μ is the mean weight (44 lbs), and σ is the standard deviation (3 lbs).
z = (40 - 44) / 3
z = -4 / 3
z ≈ -1.33
2. Look up the z-score in a standard normal distribution table or use a calculator to find the corresponding percentile.
The z-score of approximately -1.33 corresponds to a percentile of approximately 9.91%.
Therefore, approximately 9.91% of wolves weigh under 40 lbs.
To find the percentage of wolves that weigh under 40 lbs, we'll need to use the concept of standard deviation. The standard deviation measures how much the weights of wolves vary from the average weight.
First, let's calculate the Z-score for 40 lbs. The Z-score measures how many standard deviations away from the mean a particular value is. We can calculate it using the formula:
Z = (X - μ) / σ
Where:
X is the value we want to find the Z-score for (40 lbs in this case),
μ is the mean (44 lbs),
σ is the standard deviation (3 lbs).
Plugging the values into the formula:
Z = (40 - 44) / 3
Z = -4 / 3
Z = -1.33
Now we need to find the area under the standard normal distribution curve to the left of the Z-score. This area represents the percentage of wolves that weigh under 40 lbs.
You can use a Z-table or a calculator with a cumulative distribution function (CDF) function to find this value. The cumulative distribution function provides the area under the curve up to a certain Z-score.
Using a Z-table or calculator, the area to the left of -1.33 is approximately 0.0918. This means that around 9.18% of wolves weigh under 40 lbs.
Therefore, approximately 9.18% of wolves weigh under 40 lbs.