The distribution of lengths of salmon from a certain river is approximately normal with standard deviation 3.5 inches. If 10 per
2 answers:
Answer:
The value closest to the distribution's mean is 30 inches ⇒ B
Step-by-step explanation:
The z-score formula is z = (x - μ)/σ, where x represents the score, μ denotes the mean, and σ signifies the standard deviation.
Given that the lengths of salmon from a specific river follow a normal distribution with a standard deviation of 3.5 inches:
∴ σ = 3.5 inches
Since 10 percent of salmon exceed 30 inches:
- It implies P(x > 30) = 10%.
∵ 10% is equal to = 0.10.
∴ P(x > 30) = 0.10.
Utilize the normal distribution table to identify the z-score that correlates with 0.10 of the distribution's area.
∵ x = 26 inches.
- The x value is lower than 30, so the z-score will be negative.
∵ The z-score that corresponds to the area of 0.10 is -1.285.
- Insert this into the z-score formula stated above.
∴ -1.285 = (26 - μ)/3.5.
- Multiply both sides by 3.5.
∴ -4.4975 = 26 - μ.
- Add μ to both sides.
∴ μ - 4.4975 = 26.
- Add 4.4975 to both sides.
∴ μ = 30.4975.
- Round to the nearest whole number.
∴ μ ≈ 30.
∴ The closest value to the distribution's mean is 30 inches.
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Step-by-step explanation:
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Solution:
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=
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