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Each contestant in the Hunger Games must be trained to compete. Suppose that the time it takes to train a contestant has mean 5 days and standard deviation 4 days, independent of the time it takes other contestants to train. If the Hunger Games has 100 contestants to train, approximate the probability that it will take more than 250 days to train all the contestants

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Answer:

P(X>250) = 0.7357

Step-by-step explanation:

From the question we can gather the data:

μ = 5 days

σ = 4 days

n = 100

It will take more than 250 days to train the 100 contestants so,

time to train one person = 250/100 = 2.5 days.

x = 2.5 days

We will use the normal distribution formula to find the z-score and then use this z-value to find the probability from the normal distribution table.

Z = (x - μ)/(σ)

Using the values mentioned above,

Z = (2.5-5)/(4)

  = -0.625

Z = -0.63

So, using the normal distribution probability table we get the following probability at z = -0.63:

P = 0.2643

This is the probability that it will take less than 250 days to train all the contestants but we need the probability that it will take more than 250 days. So, using the total probability theorem:

P(X>250) = 1 - P(X<250)

               = 1 - 0.2643

P(X>250) = 0.7357

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