Question

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.

Answer #1

Suppose, random variable Y denotes time of eruption.

Suppose, 40th percentile for this distribution be k.

So, the
40th percentile for this distribution is
**0.40x+7.2**.

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 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 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 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...

Visitors arrive at Kid’s World entertainment
park according to an exponential inter-arrival time distribution
with mean 2.5 minutes. The travel time from the entrance to the
ticket window is normally distributed with a mean of 3 minutes and
a standard deviation of 0.5 minute. At the ticket window, visitors
wait in a single line until one of four cashiers is available to
serve them. The time for the purchase of tickets is normally
distributed with a mean of ﬁve minutes...

2) Airline accidents: According to the U.S. National
Transportation Safety Board, the number of airline accidents by
year from 1983 to 2006 were 23, 16, 21, 24, 34, 30, 28, 24, 26, 18,
23, 23, 36, 37, 49, 50, 51, 56, 46, 41, 54, 30, 40, and 31.
a. For the sample data, compute the mean and its standard error
(from the standard deviation), and the median.
b. Using R, compute bootstrap estimates of the mean, median and
25% trimmed...

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