Suppose a geyser has a mean time between eruptions of 88 minutes Let the interva

Question

Suppose a geyser has a mean time between eruptions of 88 minutes Let the interval of time between the eruptions be normally distributed with standard deviation 20 minutes Complete parts (a) through (e) below (a) What is the probability that a randomly selected time interval between eruptions is longer than 97 minutes? The probability that a randomly selected time interval is longer than 97 minutes is approximately. (b) What is the probability that a random sample of 9 time intervals between eruptions has a mean longer than 97 minutes? The probability that the mean of a random sample of 9 time intervals is more than 97 minutes is approximately. (c) What is the probability that a random sample of 22 time intervals between eruptions has a mean longer than 97 minutes? The probability that the mean of a random sample of 22 time intervals is more than 97 minutes is. (d) What effect does increasing the sample size have on the probability? Provide an explanation for this result

Explanation / Answer

a) P(X>97)=1-P(X<97)=1-P(Z<(97-88)/20)=1-P(Z<0.45)=1-0.6736=0.3264

b)for n=9; std error of mean =std deviaiton/(n)1/2 =6.667

hence P(X>97)=1-P(X<97)=1-P(Z<(97-88)/6.667)=1-P(Z<1.35)=1-0.9115=0.0885

c)for n=22; std error of mean =std deviaiton/(n)1/2 =4.264

hence P(X>97)=1-P(X<97)=1-P(Z<(97-88)/4.264)=1-P(Z<2.1107)=1-0.9826=0.0174

d) decreases ; decreases ; increases

e)

option B is correct

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.