Question

The 200 meter race times at a state track meet are normally distributed with a mean of 13.56 seconds and a standard deviation of 2.24 seconds. Using the standard normal probabilities table, what is the approximate probability that a runner chosen at random will have a 200 meter time less than 13.5 seconds?
A. 0.4880
B. 0.6331
C. 0.7422
D. 0.5714
E. 0.7910

Answer 1

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

∵ $z=\frac{13.5-13.56}{2.24}=-0.02679$

- 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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