The diameter of a pipe is normally distributed, with a mean of 0.8 inch and a variance of 0.0004. What is the probability that the diameter of a randomly selected pipe will exceed 0.84 inch? (You may need to use the standard normal distribution table. Round your answer to three decimal places.) . Hint: take the square root of the variance to find the standard deviation.

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MrRoyal MrRoyal · Answer 1 · 2022-07-27T16:57:58+02:00

The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.8

Variance = 0.0004

Calculate Standard deviation using

σ = √σ²

This gives

σ = √0.0004

Evaluate

σ = 0.2

Calculate the z-score at x = 0.84 using

z = (x - [tex]\bar x[/tex])/σ = √σ²

This gives

z = (0.84 - 0.8)/0.02

Evaluate

z = 2

The probability is then represented as:

P(x > 0.84) = P(z > 2)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.84) = 0.977

Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977