Question

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?

Answer #1

the sampling distribution of the eruptions of the Old Faithful geyser follows a Normal distribution with

(b)

Then z=(x-mean)/SD = (x-3.32)/0.3703 follows standard Normal. |

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...

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 8800 observations, the sample mean
interval was x1 = 61.2 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 24,404...

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 9200 observations, the sample mean
interval was x1 = 63.8 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 24,872...

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 9120 observations, the sample mean
interval was x1 = 62.0 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 25,106...

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 9460 observations, the sample mean interval was x1 = 62.6
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 23,000...

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 9800 observations, the sample mean
interval was x1 = 64.4 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 24,404...

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...

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 = _____ s2 = _____ s = _____
b. Based on the mean and standard deviation, would 90 minutes be
considered significantly high? Justify your...

Old Faithful in Yellowstone National Park erupts according to a
Uniform distribution. You go for a visit and wait to see an
eruption. The next eruption will happen between 12 and x minutes
after your arrival. d. Calculate the 40th percentile for this
distribution. Use formulas for your calculations, i.e. do your
calculations by hand.

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
87 minutes?
(c) What is the probability...

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