Test: Chapters 7 & 8 Test Submit Test This 27 of 30 (26 corre) This Test: 30 pts

Question

Test: Chapters 7 & 8 Test Submit Test This 27 of 30 (26 corre) This Test: 30 pts possibi pose a geyser ame time between eruptions of 83 mnutesletthe Herval of tinse bet oen he enimbemena y deub Aedwmetandard dedefen 24 mei, Conpeto Pat a teeghe belle (a) What is the probability fhat a tandomly selected time interval between eruptions is longer than 95 minules The probability that a randomly solected time interval is longer than 95 mirvutes is approximaely (Round to four decimal places as needed ) whafahe probabilty that a random sample of 6thne intervals between erupdons has a mean longer oun 95-mites? The probablity that the mean ed a random sample of 6 time intervah is more than 9s minutes is appromately[ (Round to four decimal places as needed.) lc) What is he probability that a random sample of 24 time intervals betweon oruptions has a mean longer than 95 minuties? The probatility that the mean of a random sampleot 24.ms itenals is more tan 95 minutes is appeaimately Round to Sour dedmal places as needed (d) What efect does increasing the sample size have on the probability? Provide an explanaton for this re Fill in the blanks below the population mean is less than 95 mindes, tenth, patbablity that he sample m an oth-term englon.gedr hi'n des saraple size e) What might you cenclude it a random sampla of 24 time inlervals between eplons has a mean lorger than 95 ninutes? Selet a that apply because the variablity in he sample mearn Cicx to select your answerts) Type here to search 13 2017

Explanation / Answer

Solution:- Given that mean = 83, sd = 24

a) P(X > 95) = P( Z > (95 - 83)/24 )
= P(Z > 0.5)
= 1 P(Z < 0.5)
= 1 0.6915
= 0.3085

b) 6 sample
P(X > 95) = P( Z > (95 - 83)/(24/sqrt(6) )
= P( Z > 1.2247)
= 1 P(Z < 1.2247)
= 1 0.8888
= 0.1112

c) 24 sample
P(X > 95) = P( Z > (95 - 83)/(24/sqrt(24) )
= P(Z > 2.4495)
= 1 P(Z < 2.4495)
= 1 0.9929
= 0.0071

d) If the population mean is less than 95 minutes, then the probability that the sample mean of the time between eruptions is greater than 95 minutes decreases because the variability in the sample mean decrease as the sample size increases.

e) option D. The population mean must be less than 83, since the probability is so low.

Formula:- with out sample : Z = (X-mean)/s

with sample : (X-mean)/(s/vn)

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