9. [5 pts.] Volcanic activities in a tropic island is exponentially distributed

Question

9. [5 pts.] Volcanic activities in a tropic island is exponentially distributed with a mean rate of 1 event in 50 years? a) What is the probability that the next event will occur at least 55 years from now? b) What is the mean waiting time? c What is the median waiting time? Please provide a hand-written solution. 10. [3 pts.] A certain steel bar a manufacturer produces has the mean length of 120 inches anda standard deviation of 1.6 inches. If a random sample of 50 bars selected, o atis the probabihatsni going to be 1l inche? b) What is the 80h percentile of sample mean? Please provide a hand-written solution. 11. 3 pts.] The sugar content of a one-cup serving of a certain pudding is measured for a sample of 100 servings. The sample mean and standard deviation values are 12.2 g and 0.9 g respectively. What is the 95% confidence interval of the mean sugar content of the population?

Explanation / Answer

Solution10:

mean=120

sd=1.6

n=50

P(X bar<=116)

P(Z<=116-120/1.6/sqrt(50))

P(Z<17.68)=1

ANSWER:1

SOLUTION10B:

Z SCORE FOR 80 TH PER CENTILE

Z=0.842

X-mean/sd/sqrt(n)=0.842

x-120/1.6/sqrt(50)=0.842

x-120/0.22627=0.842

x=0.842*0.22627+120

x=120.19

ANSWER:120.19

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