Question

Suppose a geyser has a mean time between eruptions of 61 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 20 minutes.Complete parts ​(a) through ​(e) below.

​(e) What might you conclude if a random sample of 35 time intervals between eruptions has a mean longer than 69 ​minutes? Select all that apply.

a)The population mean may be less than 61

b)The population mean may be greater than 61

c)The population mean must be more than 61,since the probability is so low.

d)The population mean cannot be 61,since the probability is so low.

e)The population mean is 61 and this is an example of a typical sampling result.

f)The population mean is 61 and this is just a rare sampling.

g)The population mean must be less than 61, since the probability is so low.

Answer 1

Let T be the interval of time between the eruptions.

By Central limit theorem, the sample mean follows Normal distribution with mean 61 minutes and standard deviation = 20/ = 3.38

Probability that mean longer than 69 ​minutes = P( > 69)

= P(Z > (69 - 61)/3.38)

= P(Z > 2.37]

= 0.0089

The probability is so low. So, the population mean may be greater than 61 (near to 69)

So, the following options are valid.

b)The population mean may be greater than 61

c)The population mean must be more than 61,since the probability is so low.

d)The population mean cannot be 61,since the probability is so low.