Question

Please provide all answers according to question numbers thank you

(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: A 0.3 0.4 Then P(AU B) is equal to? A0.1 0.2 (5) Suppose P(A)0.4, P(B) 0.3, and P(AnB)-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 mutually exclusive. (bEvents 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 mutually 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 S14.80. The company charges S15.50 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

Solution:-

10) The expected number of accidents on a given day is 2.15 and the approximate value of the standard deviation of the number of accidents per day is 1.5256.

$E(x)=\sum x\ast P(x)$

E(x) = 2.15

$\sigma =\sqrt{\sum P(x)\ast (x-\mu )^{2}}$

$\sigma =\sqrt{2.3275}$

$\sigma = 1.5256$