A new Term Test 1 question most days in the ADMS 2320 group chat. Try it, then check the answer here the next morning. Newest question first.
Term Test 1 is Sunday 18 October. More free help: Term Test 1 FAQ · free solved past Test 1
Friday 16 October · Ch 6 · Probability tree, Bayes (real Fall 2024 Test 1, Q2)
- The York University Bookstore's manager surveys student satisfaction. 17% of students were not satisfied with the service at their last visit.
- Of those not satisfied, only 33% return to the bookstore within a year.
- Of those satisfied, 70% return within a year.
a) What's the probability a student was not satisfied and did not return within a year? b) What's the probability a student was satisfied or did not return within a year? c) A student came back within a year. What's the probability they were satisfied? d) Knowing they returned, does the chance they were satisfied go up or down? By how much?
Answer posted tomorrow morning.
Thursday 15 October · Ch 2, 3, 4 · Frequency tables, mode, empirical rule (real Fall 2024 Test 1, Q1)
- Insomnia patients' hours slept on one night (whole numbers only). 10% of the patients slept six hours.
- 1 hour: 4 patients; 2 hours: 10; 3 hours: 18; 4 hours: ?; 5 hours: 8; 6 hours: 7; 7 hours: 5
- (d is a separate question) Daily gas sales are bell-shaped, mean 1500 L, SD 89 L.
a) How many slept four hours, and what's the mode? b) What's the total number of hours slept by all patients? c) What % slept more than 3 but less than 6 hours? d) How often are 1322 to 1678 L of gas sold in a day?
Show the answer
- a) 10% slept six hours: 7 patients = 10%, so 70 patients. 70 − 52 = 18 slept four hours. Mode: 3 and 4 both have 18, so it's bimodal (3 and 4 hours)
- b) 1(4) + 2(10) + 3(18) + 4(18) + 5(8) + 6(7) + 7(5) = 4 + 20 + 54 + 72 + 40 + 42 + 35 = 267 hours
- c) More than 3 but less than 6 means 4 or 5 hours: 18 + 8 = 26. 26 ÷ 70 = 37.14%
- d) 1322 = 1500 − 2(89) and 1678 = 1500 + 2(89). Bell-shaped, within 2 SDs: about 95% of days (empirical rule)
Answer: a) 18, bimodal (3 and 4) b) 267 hours c) 37.14% d) about 95%
Wednesday 14 October · Ch 4 · Chebyshev's theorem
- Students' weekly study hours have a mean of 12 and a standard deviation of 3.
- Nothing is known about the shape of the distribution.
At least what percentage of students study between 7.5 and 16.5 hours a week?
Show the answer
- 7.5 and 16.5 are each 4.5 hours from the mean of 12
- 4.5 ÷ 3 = 1.5 standard deviations, so k = 1.5
- Shape unknown, so use Chebyshev: 1 − 1/k² = 1 − 1/2.25 = 0.556
Answer: at least 55.6%
Tuesday 13 October · Ch 6 · Conditional probability (Bayes)
- Suppose 60% of students in a class did a full practice test.
- Of those, 80% passed Test 1.
- Of the students who didn't, only 45% passed.
- You pick a student who passed.
What's the probability they did the practice test?
Show the answer
- P(practice and pass) = 0.60 × 0.80 = 0.48
- P(no practice and pass) = 0.40 × 0.45 = 0.18
- P(pass) = 0.48 + 0.18 = 0.66
- P(practice | pass) = 0.48 ÷ 0.66 = 0.727
Answer: 0.727
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