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    "### <center>San Jose State University<br>Department of Applied Data Science</center>\n",
    "#  <center>DATA 220<br>Mathematical Methods for Data Analysis</center>\n",
    "### <center>Fall 2020<br>Instructor: Ron Mak</center>\n",
    "#  <center>MIDTERM EXAMINATION</center>\n",
    "#### <center>Six problems, each worth 25 points, 150 points total.<br><br>Open book, notes, and internet. Individual work only!<br>Be sure to explain your work in comments or by printing intermediate results.<br>You can use Python code and any Python functions.<br>You can add your own functions or other support code.<br><br>Don't forget the 25 multiple-choice questions in Canvas!</center>"
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    "#### <strong>PROBLEM 1.</strong> What is the probability that a randomly selected leap year contains 53 Sundays?"
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    "#### <strong>PROBLEM 2.</strong> The first NASA mission to land men on the moon in July 1969 brought back 64 rock samples. The rock sample had an average weight of 172 ounces on Earth with a variance of 299 ounces squared. Scientists believe that the rock population on the lunar surface does not have a normal distribution. Nevertheless, find a 99% confidence interval for the mean weight of moon rocks."
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    "#### <strong>PROBLEM 3.</strong> Pirate Jack Sparrow buried a treasure chest on one of two islands, named Palau and Nauru. Historians had long believed that it was twice as likely that the treasure is buried on Palau than on Nauru. They've just discovered a map containing directions to find the treasure! But the map is faded, and only a single letter u of the island name is still legible. Does having the map change the probability that the treasure is buried on Palau? If so, how?"
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    "#### <strong>PROBLEM 4.</strong> Accidents occur at a busy San Jose traffic intersection despite the traffic signals. Therefore, the city installed an automatic camera to photograph cars that run through red lights. After several days, the police calculated that the average number of violations per hour is 3.7. What is the probability that there will be no more than two violations during the next hour?"
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    "#### <strong>PROBLEM 5.</strong> In an exclusive Silicon Valley neighborhood, the selling prices of homes follow a normal distribution with mean \\\\$2,760,000 and standard deviation \\\\$320,000. What is the probability that the next home will sell for between \\\\$2,500,000 and \\\\$3,200,000?"
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    "#### <strong>PROBLEM 6.</strong> Suppose you have four cats named Al, Betty, Cindy, and Dan, and four cat food bowls labeled 1, 2, 3, and 4. Each bowl can hold up to twelve units of food and each cat chooses a separate bowl, but it doesn't matter which cat uses which bowl. For their dinner each day, you put twelve units of cat food into the bowls using a scoop that holds exactly one unit, so each bowl will receive a whole number units of food. In 95% of the days, some of your cats are equally hungry, so you can put the same amount of food into some of the bowls. In only 10% of the days, one or more cats aren't hungry and therefore you can leave some bowls empty. If you always put out the full twelve units of food each day, how many ways can you distribute the food among the four bowls?"
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