Question

Adult racehorse weights are normally distributed, with a mean of 500 kg and a standard deviation of 33 kg. Approximately what percentage of the adult racehorses weigh more than 570 kg?
1.7%
98.3%
93.3%
0.12%

Answer 1

The percentage of the adult racehorses weigh more than 570 kg is

1.7% ⇒ 1st answer

Step-by-step explanation:

Adult racehorse weights are normally distributed, with a mean of

500 kg and a standard deviation of 33 kg

We need to find the percentage of the adult racehorses weigh more

than 570 kg

To solve the problem do these steps

1. Find z-score

2. Use z-score to find the corresponding area which represented P(x)

3. Change P(x) to percentage

∵ z = (x - μ)/σ

∵ The mean μ = 500 kg

∵ The standard deviation σ = 33 kg

∵ x = 570 kg

Substitute these values in the rule above

∴ z = $\frac{570-500}{33}=2.12$

Let us use the normal distribution table to find the corresponding area

∵ The area corresponding to z-score of 2.12 is 0.98300

∵ We need x > 570 , then we need the area to the right of the z-score

∴ P(x > 570) = 1 - 0.98300 = 0.017

Change it to percentage by multiplying the answer by 100%

∴ The percentage of x > 570 = 0.017 × 100% = 1.7%

The percentage of the adult racehorses weigh more than 570 kg is

1.7%

Learn more:

You can learn more about the normal distribution curve in brainly.com/question/6073431

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