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Calculate the five-number summary, and find IQR.
x 1 3 5 10 20
P(X) 0.16 ? 0.22 0.22 0.08
a) What is the probability that a 1st grader spends exactly 3 dollars?
b) Calculate the expected value, variance, and standard deviation of the random variable X?
(a) What is the probability that a set of tires wears out before 20,000 miles?
(b) What is the probability that the manufacturer turns a profit on selling a set to one customer?
(c) If the manufacturer sells 500 sets of tires, what is the probability that it earns a profit after paying for any replacements? Assume that the purchases are made around the country and that the drivers experience independent amounts of wear.
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(a) Under these conditions, what is the probability that none of the 12 animals in this herd ate the tasty weeds?
(b) Does the Poisson model give a good estimate of the probability that no animal ate the weed?
Question 1. Historically a bank expects about 5% of its borrowers to default (not repay). The bank currently has 250 loans outstanding.
(a) In order to use a binomial model to compute the probabilities associated with defaults, what must the bank assume about the behavior of these borrowers?
(b) Do the necessary assumptions listed in part (a) appear reasonable in the context of this problem?
(c) The bank has reserves on hand to cover losses if 25 of these loans were to default. Will these reserves will be enough?
52 33 70 95 57 61
57 64 54 94 38 61
50 39 94 63 59 31
68 88 93 48 82 82
74 70 92 76 98 91
32 33 31 75 54 48
36 64 63 66 92 98
36 54 71 86 84 55
91 34 64 67 89 78
97 92 53 56 68 55
93 42 51 77 36 93
44 66 63 33 68 79
83 53 86 76 35 40
55 41 36 39 42 96
60 53 38 51 95 56
48 69 49 33 95 37
83 62 96 34 85 32
39 59 77 62 35 34
54 89 36 45 83 34
39 61 88 86 55 33
69 54 30 38 79 77
95 34 38 91 80 90
88 45 95 71 80 43
61 40 31 61 58 53
91 63 60 94 98 53
50 34 75 74 90 98
1. Make the frequency distribution table with appropiate class interval, frequency,
cumulative frequency.
2. Calculate the standard deviation, variance and range
3. Make the following diagrams: Histogram, Frequency Polygon, Ogive
a) At least how many percent of students scored between 150 to 180.
b) Assuming the histogram of GPA has a right skewed distribution, calculate the range of GPA that will cover at least 71% of the students?
c) Assuming the histogram of GPA follows the normal distribution, approximately how many students score between 147 to 159?
a) Suppose the doctor wants to construct a confidence interval for the proportion of all the patients who have brain cancer and survived at least 3 years, what is the preliminary conditions that need to be verified and what can we assume once the conditions are satisfied?
b) Construct a 86% confidence interval for the proportion of all patients who have brain cancer and survived at least 3 years, and state the confidence statement.
1. The lifetime of light bulbs produced by a company are normally distributed with mean 1000 hours and standard deviation 130 hours.
a) The top 30% of all light bulbs should last at least how many hours?
b) What is the probability that a randomly selected light bulb will last at least 900 hours?
c) If we randomly select 8 light bulbs, what is the probability that the average of these light bulbs will last more than 1050 hours?
