Question

Suppose a geyser has a mean time between eruptions of 70 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 18 minutes.

(a) What is the probability that a randomly selected time interval between eruptions is longer than 79 ​minutes?
​(Round to four decimal places as​ needed.)
​(b) What is the probability that a random sample of 88 time intervals between eruptions has a mean longer than 79 ​minutes?
​(Round to four decimal places as​ needed.)
​(c) What is the probability that a random sample of 27 time intervals between eruptions has a mean longer than 79 ​minutes?
​(Round to four decimal places as​ needed.)

Answer 1

P(x > 83) = P(z > 9/20) = normalcdf(9/20,100) = 0.3264

Answer 2

Explanation:

Let X be the geyser mean time between eruptions of 70 minutes.

X is N (70, 19)

a)
`P(X<79) = P(Z<(79-70)/(18) )=P(Z<0.5)\\=0.6915`

b) Sample size =88. Std error =
`(19)/(√(88) ) =2.025`

`P(X>79) = P(Z>4.086)= 0.0000`

c) For sample size =27, std error =
`(19)/(√(27) ) =3.66`

P(X>79) = P(Z>2.46) =0.5-0.4931=0.0069