# Cheat Sheet for Statistics 1

Submitted By grumpycat
Words 9115
Pages 37
Question 1 # sold | P(x) | 0 | 0.1 | 1 | 0.11 | 2 | 0.2 | 3 | 0.23 | 4 | 0.3 | 5 | 0.06 |
Question 2: The average rate of occurrence of accidents was 8.15 per week. A) during that time, what is the probability of getting less than 3 accidents a week? Use poisson for this question. Since it is less that 3 accidents, x = 0,1,2 (Px=o) = [(8.15^0) (e^8.15)] / 0! = 0.00288735. (Px=1) = [(8.15^1) (e^8.15)] / 1! = 0.002353193. (Px=2) = [(8.15^2) (e^8.15)] / 2! = 0.009589362. Add all these results together, and p(x<3) is 0.01223119. B) The probability if an accident on the road is 0.295. Out of 10 reportable accidents, what is the probability that 2 occurred on the road? Use Binomial for this. Since it is exactly 2, we need to find P(x=2). Use the binomial formula, n = 10, x = 2, p = 0.295, and q is 0.705.
= 10!/2!(10-2)! * 0.205 ^2 * q^ 10-2. Answer is 0.23898436.
Question 3: 15% of drivers have a probationary license and 85% have a regular license. In a given year, 10% of drivers with probationary licenses are involved in an accident. 2.5% of regular drivers are involved in an accident. For this question it is better to draw a tree diagram.

Question 4: Mean values for income for men are 100K, for woman, 80K. SD deviations of 20K and 15K respectively. Variables are normally distributed and independent.
Calculate the 95th percentile, for men income. 95th p = 0.95. In the zscore table, we find a value of 1.64. Us e the formula for z-score (population) : 1.64 = x -100/ 20. Solve for 132.8K
Calculate the Q1, Q3, and the IQR for women’s income. Q1 = 0.25. Z score of 0.67. Us e the formula for z-score (population) : 0.67 = x -80/ 15. Solve for 69.95K. Q3= 0.75. Z score of 0.67. Us e the formula for z-score (population) : 0.67 = x +80/ 15. Solve for 90.05. IQR is Q3-Q1. = 20.1K.
What are the probabilities of a man having an income of more than...

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