The approximate probability that a runner chosen at random will have a 200 meter time less than 13.5 seconds is 0.4880 ⇒ A
Step-by-step explanation:
To find the probability of a random variable X which has a normal distribution do that
- If X < b, find the z-score using the formula z = (b - μ)/σ, where μ is the mean and σ is the standard deviation
- Use the normal distribution table of z to find the corresponding area to the left of z-score
∵ The 200 meter race times at a state track meet are normally
distributed with mean of 13.56 seconds and a standard deviation
of 2.24 seconds
∴ μ = 13.56
∵ σ = 2.24
- We need to find the probability that a runner chosen at random
will have a 200 meter time less than 13.5 seconds
∵ X < 13.5
∴ b = 13.5
- Find z-score
∵ [tex]z=\frac{13.5-13.56}{2.24}=-0.02679[/tex]
- Use the normal distribution table to find the area corresponding to z
∵ The corresponding area of z ≅ -0.03 is 0.4880
∴ P(x < 13.5) = 0.4880
The approximate probability that a runner chosen at random will have a 200 meter time less than 13.5 seconds is 0.4880
Learn more:
You can learn more about the probability in brainly.com/question/4625002
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