Due Date and Time: Sunday, November 14th,11:59 pm EDT Written Questions 1. Leo is a very active dog that requires long walks at least 3 times a day. Assume that the following is the distribution of...

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Due Date and Time: Sunday, November 14th,11:59 pm EDT Written Questions 1. Leo is a very active dog that requires long walks at least 3 times a day. Assume that the following is the distribution of the number of times Leo goes for long walks. x 3 4 5 p(x) 0.1 0.6 0.3 Assume that the number of times Leo goes for long walks is independent from day to day. A. Find the sampling distribution of the mean number of times Leo goes for walks of two randomly selected days. That is, n=2. Hint: Let ?1, ?2 be the number of times Leo goes for walks in the first and second randomly selected days. You are asked to determine the sampling distribution of �̅� = ?1+?2 2 . B. What is the sampling distribution of the mean of 40 randomly selected days (n=40)? C. What the probability that the average of 40 randomly selected days is more than 4.1? 2. A vaccine is found to be 85% effective in preventing a certain disease. The vaccine is given to 40 people. A. Approximate the probability that the vaccine is effective for no more than 30 of the people who received it? B. Approximate the probability that the vaccine will be effective for at least 32 and at most 38 people who received it? 3. Assume that the wait time to see your family doctor is uniformly distribution been 10 and 30 minutes. A. What’s the probability you wait more than 20 minutes to see your family doctor? B. What’s the probability you less than 15 minutes to see your family doctor? C. What’s the probability you wait between 20 and 25 minutes? 4. The systolic blood pressure reading for a person varies throughout the day. Assume that for a certain person their readings follow a normal distribution with mean 120mmHg and standard deviation 25mmHg. A. What’s the probability that a blood pressure reading for the person with the distribution above is between 110 and 125? B. What’s the probability that a blood pressure reading for the person with the distribution above is less than 130? C. If a person’s systolic blood pressure is more than 140, they are considered hypertensive. What’s the probability that a single reading would indicate that this person is hypertensive? 5. Assume that the lifetime of a certain type and brand of TV is exponentially distributed with mean 8 years. A. What’s the probability a TV of this type and brand lasts longer than 6 years? B. What’s the probability a TV of this type and brand less than 7 years? C. How long do 90% of TVs of this type and brand last? SPSS Questions – USE SPSS ONLY WHEN INSTRUCTED Suppose that the probability distribution for a population is exponential with mean 2. You will be using this distribution for all the questions below. 1. Use SPSS to generate 10,000 observations from this distribution. Don’t include the data you generate with your assignment. A. Construct a histogram for the data you generated and comment on the distribution shape. Include the histogram with your assignment. B. Find the mean and the variance. Comment on both (compare them to the true mean and variance). Include the summary table with the mean and variance you obtain from SPSS. 2. Use SPSS to generate 1,000 samples of size 5 (n=5) from the distribution described above. Don’t include the data you generate with your assignment. A. Find the mean of each of the 1,000 samples and construct a histogram for the 1,000 means you obtain. Comment on the shape of the distribution. Explain why the means have the distribute you observe. Include the histogram with your assignment only. 3. Use SPSS to generate 1,000 samples of size 100 (n=100) from the distribution described above. Don’t include the data you generate with your assignment. A. Find the mean of each of the 1,000 samples and construct a histogram for the 1,000 means you obtain. Comment on the shape of the distribution. Explain why the means have the distribute you observe. Include the histogram with your assignment only. B. Find the mean and the variance for the 1,000 means. Comment on both (compare them to the true mean and variance). Include the summary table with the mean and variance you obtain from SPSS.