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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.)

Respuesta :

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

Answer:

Step-by-step explanation:

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

X is N (70, 19)

a)[tex]P(X<79) = P(Z<\frac{79-70}{18} )=P(Z<0.5)\\=0.6915[/tex]

b) Sample size =88. Std error = [tex]\frac{19}{\sqrt{88} } =2.025[/tex]

[tex]P(X>79) = P(Z>4.086)= 0.0000[/tex]

c) For sample size =27, std error = [tex]\frac{19}{\sqrt{27} } =3.66[/tex]

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