# 1. One question that meteorologists get a lot goes something like this

August 31, 2017

Question
1. One question that meteorologists get a lot goes something like this: “Last winter was snowy, does that mean this winter will be snowy too?” Basically, this question explores the idea of whether snowfall during a given winter depends on how much it snowed the previous winter. Here, you will investigate this idea using snowfall data from State College. Consider the following data:

1896-97 31.4
1897-98 37.5
1898-99 53.5
1899-00 26.8
1900-01 38.5
1901-02 59.6
1902-03 34.1
1903-04 38.2
1904-05 48.0
1905-06 36.6
1906-07 57.1
1907-08 67.7
1908-09 42.5
1909-10 66.4
1910-11 55.0
1911-12 47.0
1912-13 20.4
1913-14 77.4
1914-15 55.7
1915-16 44.8
1916-17 39.1
1917-18 59.9
1918-19 17.6
1919-20 54.1
1920-21 30.2
1921-22 39.5
1922-23 65.4
1923-24 41.7
1924-25 41.1
1925-26 48.3
1926-27 41.4
1927-28 64.8
1928-29 21.3
1929-30 21.5
1930-31 28.0
1931-32 28.4
1932-33 22.1
1933-34 31.1
1934-35 42.7
1935-36 75.4
1936-37 31.4
1937-38 20.2
1938-39 42.4
1939-40 41.4
1940-41 45.9
1941-42 74.9
1942-43 42.0
1943-44 36.4
1944-45 52.5
1945-46 29.5
1946-47 44.7
1947-48 42.5
1948-49 30.8
1949-50 34.5
1950-51 52.4
1951-52 41.9
1952-53 31.7
1953-54 35.0
1954-55 26.1
1955-56 37.0
1956-57 57.2
1957-58 58.1
1958-59 44.7
1959-60 47.7
1960-61 91.8
1961-62 52.2
1962-63 61.2
1963-64 78.2
1964-65 46.2
1965-66 43.2
1966-67 59.5
1967-68 40.6
1968-69 38.9
1969-70 90.5
1970-71 68.4
1971-72 54.2
1972-73 29.5
1973-74 40.9
1974-75 50.1
1975-76 42.9
1976-77 41.1
1977-78 98.2
1978-79 39.9
1979-80 17.9
1980-81 38.8
1981-82 69.1
1982-83 22.6
1983-84 50.2
1984-85 31.6
1985-86 42.3
1986-87 52.3
1987-88 39.0
1988-89 23.7
1989-90 40.8
1990-91 34.4
1991-92 26.9
1992-93 92.5
1993-94 109.3
1994-95 23.5
1995-96 99.0
1996-97 41.4
1997-98 48.2
1998-99 35.2
1999-00 19.8
2000-01 32.1
2001-02 21.7
2002-03 83.6
2003-04 71.4
2004-05 36.5
2005-06 26.9
2006-07 37.6
2007-08 43.2
2008-09 26.3
2009-10 49.1
2010-11
38.4

which gives winter snowfall data for State College going back to the winter of 1896-97 (a total of 115 winters). Fifty inches of snow in one winter is not all that common in State Collge,and most folks living here would consider a winter with that much snow a “snowy winter.” With that in mind, define Event A as fifty inches or more of snow in StateCollege in winter. Use the data to answer the following:

a. Estimate Pr {A}.

b. Estimate Pr {A | previous winter had 50 inches of snow or more } .

c. Estimate Pr {A | previous winter had less than 50 inches of snow }.

d. Do your estimates of conditional probability suggest there’s a positive statistical dependence from one winter to the next in the snowfall data? (i.e., is the conditional probability of a snowy winter given the previous winter was snowy high than the unconditional probability of a snowy winter). Justify your answer.

2. The International Space Station (ISS) orbits 350 km up, but the ISS is so large that it can be seen from Earth with the naked eye, if you know when and where to look. For this problem, assume that on a clear night, a properly trained observer has a 93% chance of seeing the ISS when it passes overhead.

Assume that the ISS will be passing overhead tonight in State College, and skies will be clear. Eight (properly trained) members of the Penn State Astronomy Club position themselves at eight different locations in State College, each independently attempting to see the ISS.

a. What is the probability that all eight members of the club will see the ISS tonight?

b. What is the probability that none of the members of the club will see the ISS tonight? For this part of the problem, keep 5 decimal places accuracy in your answer.

c. AccuWeather at State College predicts that there is a 30% chance of raining or being cloudy when ISS will be passing State College tonight. If it is raining or cloudy, the probability of seeing the ISS is zero. Now what is the probability that all eight members of the club will see the ISS tonight? What is the probability that at least one of the members of the club will see the ISS tonight?

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