Question

The following data are the lengths of time (in minutes) between eruptions for a sample of eruptions of the Old Faithful geyser in Yellowstone National Park. 83 76 86 82 87

a. Calculate the mean, variance, and standard deviation for the data. Be sure to follow the rounding conventions and include the correct units!

X = _____ s^{2} = _____ s = _____

b. Based on the mean and standard deviation, would 90 minutes be considered significantly high? Justify your answer.

Answer #1

tabulating the values,we get

sample mean = 82.8 minutes

sample variance = 18.7 minutes

sample standard deviation = 4.324 minutes

mean + 2xs = 82.8+2x4.324 = 91.448

if we assume the populaton to be normally distrbuted then, as per empirical rule, almost 95% of data value lie within 2 standard deviations from mean.

since, 90 lies within 2 standard deviaton from mean so, its not significantly higher and well wthin the usual range.

In a sample of 500 eruptions of the Old Faithful geyser at
Yellowstone National Park, the mean duration of the eruptions was
3.32 minutes and the standard deviation was 2.09 minutes. A random
sample of size 30 is drawn from this population.
a. Describe the sampling distribution of the eruptions of the
Old Faithful geyser.
b. What is the probability that the mean duration of eruptions
is between 2.5 minutes and 4 minutes?

The following are 30 time lapses in minutes between eruptions
of Old Faithful geyser in Yellowstone National Park, recorded
between the hours of 8 a.m. and 10 p.m. on a certain day, and
measured from the beginning of one eruption to the beginning of the
next:
68, 63, 66, 63, 61, 44, 60, 62, 71,
62, 62, 55, 62, 67, 73, 72, 55, 67, 68, 65,
60, 61, 71, 60, 68, 67, 72, 69, 65,
66
A researcher wants to...

Suppose a geyser has a mean time between eruptions of 86 minutes
Let the interval of time between the eruptions be normally
distributed with standard deviation 26 minutes
.
(a) What is the probability that a randomly selected time
interval between eruptions is longer than 99 minutes?
(b) What is the probability that a random sample of 9 time
intervals between eruptions has a mean longer than 99 minutes?

The U.S. Geological Survey compiled historical data about Old
Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let
x1 be a random variable that represents the time interval (in
minutes) between Old Faithful eruptions for the years 1948 to 1952.
Based on 9160 observations, the sample mean interval was x1 = 61.8
minutes. Let x2 be a random variable that represents the time
interval in minutes between Old Faithful eruptions for the years
1983 to 1987. Based on 23,351...

Suppose a geyser has a mean time between eruptions of 86
minutes. Let the interval of time between the eruptions be normally
distributed with standard deviation 19 minutes. Complete parts (a)
through (e) below.
(a) What is the probability that a randomly selected time
interval between eruptions is longer than 94 minutes?
(b) What is the probability that a random sample of 9 time
intervals between eruptions has a mean longer than 94 minutes?
(c) What is the probability that...

Suppose a geyser has a mean time between eruptions of 75
minutes. Let the interval of time between the eruptions be normally
distributed with standard deviation
26 minutes. Complete parts (a) through (e) below
(a) What is the probability that a randomly selected time interval
between eruptions is longer than
87 minutes?
(b) What is the probability that a random sample of 13 time
intervals between eruptions has a mean longer than
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(c) What is the probability...

The following are the interval times? (minutes) between
eruptions of a geyser. Detemine the five number summary and
construct a box plot from the data below.
83?84??85???87??89??90??91??92??94??97???97??98???99???104??106?109
The number 5 summary is?

Suppose a geyser has a mean time between eruptions of 70
minutes
If the interval of time between the eruptions is normally
distributed with standard deviation 20 minutes
answer the following questions.
(a) What is the probability that a randomly selected time
interval between eruptions is longer than
80 minutes?
The probability that a randomly selected time interval is longer
than 80 minutes is approximately?

Suppose a geyser has a mean time between eruptions of 84
minutes. If the interval of time between the eruptions is normally
distributed with standard deviation 27 minutes A. Whats the
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Suppose a geyser has a mean time between eruptions of 85
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The probability that the mean of a random sample of 9 time
intervals is more than 96 minutes is approximately _______.
(Round to four decimal places as needed.)

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