(Solved): Part 3!! (1) Ana has started her own company, Imprint Shirts, which makes Custom Embroidered Logo po ...

(1) Ana has started her own company, Imprint Shirts, which makes Custom Embroidered Logo polo shirts for speoal orders. Since she has just begun this operation, she rents the equipment from a local shop when necessary. The cost of using the equipment is \( \$ 2,880 \). The materials used in one shirt cost \( \$ 11 \), while the labor cost is \( \$ 8 \) per 13,160 (2) Let \( C= \) Event \( C \) and \( E= \) Event \( E \). Then, for independent events: \( P(C E)=P(C) \cdot P(E) \) and \( P(C / E)=P(C) \) (a) For dependent events: \( P(C E)= \) and \( P(C / E)= \) (b) For mutually exclusive events: \( \quad P(E \) or \( X)= \) (c) For mutually inclusive (not exclusive) events: \( P(E \) or \( X)= \) (3) Two events, \( A \) and \( B \), are independent, with \( P(A)=0.4 \) and \( P(B)=0.2 \). (a) Find \( P(A B) \). \( P(A B)= \) (b1) Are events \( A \) and \( B \) mutually exclusive? (Y for yes or \( \mathrm{N} \) for no). (b2) Explain your answer (4) There are 36 questions on a multiple-choice test. Ted belleves he has a \( 70 \% \) chance of answering for each of these questions correctly. Write an Excel formula to find the probability he gets 25 or more questions correct. \( = \) As an example, what is the probability Ted gets 20 questions correct? Answer: BINOM.DIST(20,36,0.7,FAISE) (5) The time to complete a construction project is normally distributed with a mean of 285 days and a standard dev. of 17 days. Find the probability (rounding to 5 decimal places) the project will take more than 275 days using the Standard Norami table (Appendix A). Let \( X \) be the construction project completion time.