A distant Volcano you’re observing has a mean time between eruptions of 70 minut

Question

A distant Volcano you’re observing has a mean time between eruptions of 70 minutes. If the interval of time between eruptions is normally distributed with a standard deviation of 18.5 minutes, what is the probability that a random sample of 25 time intervals between eruptions has a mean longer than 80 minutes? Please Show your work. A distant Volcano you’re observing has a mean time between eruptions of 70 minutes. If the interval of time between eruptions is normally distributed with a standard deviation of 18.5 minutes, what is the probability that a random sample of 25 time intervals between eruptions has a mean longer than 80 minutes? Please Show your work.

Explanation / Answer

here, mean = 70 , std. deviation = 18.5 , n = 25 , X = 80

By normal distribution formula,

z = ( x - mean) / (std. deviation / sqrt(n) )

= ( 80 - 70) / ( 18.5 / sqrt(25))

= 2.702

We need to find P(Z > 2.702) by standard right tail, we get

P(X > 80) = P(z >2.702) = 0.0034

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