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STAT 160-991 Assignment 1 (based on Handouts 1 - 8) (1) Which of the following statements applies to this set of data values: 17, 15, 16, 14, 17 18, and 22? (a) The mean, median, and mode are all equal. b) Only the mean and median are equal. (c) Only the mean and mode are equal. (d) Only the median and mode are equal (2) A sample of students who have taken a calculus test has a mean score of 78.2, a mode of 67, and a median score of 67. Based on this information, what may one deduce about the distribution of the test scores? (a) It is symmetric. (b) It is right-skewed. (c) It is left-skewed. (d) It is bimodal. (3) What is the set of all simple events of an experiment called? (a) a population (b) a distribution (c) a sample space (d) a random sample 4) For two events A and B, suppose: A0.3 0.4 Then P(AU B) is equal to? A 0.1 0.2 0.3, and P(An B) (5) Suppose P(A) 0.1, P(B) 0.12, which one of the following statements correctly defines the relationship between events A and B? (a) Events A and B are independent, but not mtually exclusive (b) Events A and B are mutually exclusive, but not independent (c) Events A and B are neither mutually exclusive nor independent. d) Events A and B are both mutully exclusive and independent (6) Suppose P(A) 0.80, P(B)-0.60 and P(AUB)-0.90. Then what is the value of P(AIB)? (7) From experience, a shipping company knows that the cost of delivering a small package within 24 hours is $14.80. The company charges $15.50 for shipment but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 2% of its packages within the 24-hour period what is the expected gain per package?

Answer 1

1)

mean =    ΣX/n =    119.000   /   7   =   17

mode= highest frequency data =    17
Median=0.5(n+1)th value =    4th   value of sorted data
=   17

answer: the mean, median and mode are all equal

2)

mean>median , it is right skewed

3)

a sample space

4)

P(A u B) = 0.1+0.3+0.4=0.8

5)

P(A)*P(B) = 0.4*0.3 = 0.12   

P(A n B) = 0.12

P(A)*P(B) = P(A n B)
answer: event A and B are independent but not mutually exclusive  

6)

P(A n B)=P(A)+P(B) - P(Au B) = 0.8+0.6-0.9=0.5      
P(A|B) = P(A n B)/P(B) = 0.5/0.6=   0.833