The most famous geyser in the world, Old Faithful in Yellowstone National Park,

Question

The most famous geyser in the world, Old Faithful in Yellowstone National Park, has mean time between eruptions of 85 minutes. Past research has shown that the population standard deviation is known to be 21.25 and that the distribution of time between eruptions is bimodal.

a)What is the probability that a random sample of 35 time intervals between eruptions has a mean longer than 93 minutes?

b)What is the probability that a random sample of size 15 time intervals between eruptions has a mean longer than 93 minutes?

Explanation / Answer

Mean ( u ) =85
Standard Deviation ( sd )=21.25
Number ( n ) = 35
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
a)
P(X > 93) = (93-85)/21.25/ Sqrt ( 35 )
= 8/3.592= 2.2272
= P ( Z >2.2272) From Standard Normal Table
= 0.013                  

b)
P(X > 93) = (93-85)/21.25/ Sqrt ( 15 )
= 8/5.487= 1.4581
= P ( Z >1.4581) From Standard Normal Table
= 0.0724                  

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.