g ten random numbers are drawn from a standard normal distribution. what is the probability that at least one will exceed 2.66? round your answer to three decimal places.

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15-12-2022
Mathematics

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g ten random numbers are drawn from a standard normal distribution. what is the probability that at least one will exceed 2.66? round your answer to three decimal places.

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contexto1019 contexto1019 · Answer 1 · 2022-12-20T06:50:39+01:00

The probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.

This can be calculated using the complementary probability formula, which is 1 - P(x ≤ 2.66), where P(x ≤ 2.66) is the probability that all ten numbers are less than or equal to 2.66.

The probability that all ten numbers are less than or equal to 2.66 can be calculated using the normal distribution function, which gives the probability that a random variable x follows a normal distribution with mean μ and standard deviation σ. For a standard normal distribution, the mean is 0 and the standard deviation is 1, so the probability that all ten numbers are less than or equal to 2.66 can be calculated as:

P(x ≤ 2.66) = Φ(2.66)^10

where Φ(x) is the normal distribution function.

Substituting this value into the complementary probability formula, we get:

1 - P(x ≤ 2.66) = 1 - Φ(2.66)^10 = 0.045

Thus, the probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.

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