Suppose a geyser has a mean time between eruptions of 68 minutes. Let the interv

Question

Suppose a geyser has a mean time between eruptions of 68 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 21 minutes. Complete parts (a) through (e) below. (a) What is the probability that a randomly selected time interval between eruptions is longer than 78 minutes? Round to four decimal places as needed.) (b) What is the probability that a random sample of 12 time intervals between eruptions has a mean longer than 78 minutes? The probability that the mean o arar do sample of 12 tre intervals is more than 78 minutes is approximately Round to four decimal places as needed.) (Round to four decimal places as needed.) (d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. Fillin the blanks below the populat mean is less than 78 mutes, then the probability that the sample mean of the time between er because the variability in the sample mearn ons is greater than 78 minutes population mean cannot be 68, since the probabilty is so low. The population mean may be less than 68 A B. Click to select your answer(s). ary 03/11/18 11:59pm

Explanation / Answer

a)

Z = (X - 68)/21

P ( X>78 )=P ( Z>0.48 )

= 0.3156

b)

Z = (Xbar - 68)/(21/sqrt(12))

p(x> 78)

= P (Z>1.65)=0.0495

c)

Z = (Xbar - 68)/(21/sqrt(18))

P(x> 78)

=P (Z>2.02)=0.0217

d)

decreases , decreases , increases

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