Question

Suppose a geyser has a mean time between eruptions of 76 minutes . If the interval of time between the eruptions is normally distributed with standard deviation 27 minutes ​, answer the following questions.

(b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 87 minutes?

(c) What is the probability that a random sample of 100 time intervals between eruptions has a mean longer than 120 ​minutes?

(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result.

​(e) What might you conclude if a random sample of

100 time intervals between eruptions has a mean longer than 120 minutes?

Answer 1

Here we have : = 76, = 27

The interval of time between the eruptions is normally distributed.

b) Here we have n= 13.

We need to find, time intervals between eruptions has a mean longer than 87 minutes.

p ( > 87 )

= p ( z > 1.47 )

= 1 - p ( z 1.47 )
= 1 - 0.9292 ---------------( using excel formula " =norm.s.dist(1.47,1) " )

= 0.0708

c)

Here we have n= 100.

We need to find, time intervals between eruptions has a mean longer than 120 minutes.

p ( > 120 )

= p ( z > 16.30 )

= 1 - p ( z 16.30 )
= 1 - 0.99999 ---------------( using excel formula " =norm.s.dist(16.30,1) " )

= 0.00001

d) Increasing sample size, reduces variations. This reduces chances of mean time intervals between eruptions has more than 120 minutes.

e) Probability that random sample of 100 time intervals between eruptions has a mean longer than 120 minutes is very very less. This might be unusual.