Answer :
The weight of a polar bear at the 30th percentile is approximately 145.66 kg.
Option B is answer.
Given:
- Mean weight (μ) = 179 kg
- Standard deviation (σ) = 63 kg
Step 1: Find the z-score corresponding to the 30th percentile.
Using a standard normal distribution table or calculator, the z-score for the 30th percentile is approximately -0.5244.
Step 2: Use the formula for z-score to find the weight (x) at the 30th percentile.
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
where:
- z is the z-score
- x is the weight at the 30th percentile
- μ is the mean weight
- σ is the standard deviation
Substitute the values:
[tex]\[ -0.5244 = \frac{x - 179}{63} \][/tex]
Step 3: Solve for x.
Multiply both sides by 63:
[tex]$$ -0.5244 \times 63 = \frac{x - 179}{63} \times 63 $$[/tex]
[tex]$$ -33.3372 = x - 179 $$[/tex]
Add 179 to both sides:
-33.3372 + 179 = x
x = 145.6628
Therefore, the weight of a polar bear at the 30th percentile is approximately 145.66 kg.
Option B is answer.
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Question:
A biologist is studying the weights of female polar bears in the Arctic and finds that the mean weight is 179 kg with a standard deviation of 63 kg. Assume weights are normally distributed. What is the weight of a polar bear at the 30th percentile?
A. 158.33 kg
B. 145.66 kg
C. 167.24 kg
D. 212.03 kg
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