ONLY NEED (d) and (e) Suppose a geyser has a mean time between eruptions of 67 m
ID: 3374454 • Letter: O
Question
ONLY NEED (d) and (e)
Suppose a geyser has a mean time between eruptions of 67 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 18 minutes.
Complete parts ?(d) and ?(e) below.
a) The probability that a randomly selected time interval is longer than 76 minutes is approximately 0.3085.
b) The probability that the mean of a random sample of 8 time intervals is more than 76 minutes is approximately
0.0793
c) The probability that the mean of a random sample of 19 time intervals is more than 76 minutes is approximately
0.0146
d) What effect does increasing the sample size have on the? probability? Provide an explanation for this result. Fill in the blanks below.
If the population mean is less than 76 ?minutes, then the probability that the sample mean of the time between eruptions is greater than 76 minutes ______ because the variability in the sample mean _____ as the sample size ______.
(e) What might you conclude if a random sample of 19 time intervals between eruptions has a mean longer than 76
?minutes? Select all that apply.
A. The population mean may be greater than 67.
B. The population mean must be less than 67?, since the probability is so low.
C. The population mean is 67?, and this is an example of a typical sampling result.
D. The population mean must be more than 67?, since the probability is so low.
E. The population mean cannot be 67?, since the probability is so low.
F. The population mean may be less than 67.
G. The population mean is 67?, and this is just a rare sampling.
Suppose a geyser has a mean ime between eruptions of 67 minutes Let the inerval of sme between the eruptions be normaly astrouted wth standand deviation 18 minutes Complete parts (aj through e below a) what s the probuablty hat a randomly selecled tme interval between eruptions is longer than 76 minutes? The prcbability that a randomly selected time inmerval is longer than 76 minules is approximately Round to tour oecimal places as needed) p) what ts the probability that a candom sample of 8 time intervals behween eruptions has a mean longer than 6 minutes The probabilily thait the mean of a random sample of 8 ime intervats is more than 76 miautes is approximatey Round to four deoimal places as needed ) (e) what is he probabity that a random sample of 19 tme ervals beteeen eruptions has a mean longer than 76 miutes? The probabaity that ne mean of a random sample of 19 me intervals s more than 76 mnutes is approximalely Round to tour deomal places as needed ) id) What effect does inceasng the sanple sace have on the probability? Pvide an expianantion for thn resu Fain the blanks bebw becaune ne abaty n the sample mean as the sanpe se CA. The population mean may be greater hn 67 B The popuiation mean must be less than 67, snce the probabiity is so low ®c. D. The The poputat on mean is67, andthis is an examp e ot atypical samping iesu poputation nean must be more than 67, since the probabaity is so low E. The population mean cannot be 6T, since the probabiaty is so low F. The poputation mean may be less than 67 G. The popuaion mean is 67, and es is pst a rare sampingExplanation / Answer
d)
If the population mean is less than 76 ?minutes, then the probability that the sample mean of the time between eruptions is greater than 76 minutes decreases because the variability in the sample mean decreases as the sample size increases
e)
A. The population mean may be greater than 67.
G. The population mean is 67?, and this is just a rare sampling
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