36. Basketball Suppose you make 90% of your free throws and you attempt 3 free throws. Use the Binomial Theorem to calculate each probability.

    1. You do not make any of them.
    2. You only make 1 of them.
    3. You only make 2 of them.
    4. You make all of them.
37. Genetics About 11% of the general population is left-handed. At a school with an average class size of 30, each classroom contains four left-handed desks. Does this seem adequate? Justify your answer.
38. Open-Ended Describe a binomial experiment that can be solved using the expression   7 C 2 ( 0.6 ) 2 ( 0.4 ) 5 . sub 7 , cap c sub 2 . open 0.6 close squared . open 0.4 close to the fifth . .
39. Graph each probability distribution for ( p + q ) 3 . open p plus q close cubed . .
    1. p = 0.9 , q = 0.1 p equals 0.9 comma q equals 0.1
    2. p = 0.45 , q = 0.55 p equals , 0.45 , comma q equals , 0.55
    3. Compare and Contrast How are the graphs in parts (a) and (b) similar? How are they different?

C Challenge

Statistics A multiple-choice test has ten questions. Each question has five choices, with only one correct answer.

40. Statisticians consider a “rare” event to have less than a 5% chance of occurring. According to this standard, what grades would be rare on this test if you guess? Justify your answer.
41. Design and conduct a simulation to model this situation. Gather results of simulations from your classmates. Do these results confirm the grades you identified as rare in Exercise 40? Explain.
42. Pascal's Triangle The nth row of Pascal's triangle has n + 1 terms. Find   8 C 4 . sub 8 , cap c sub 4 , .  What row and term does this value represent in Pascal's Triangle? Use combinations to find the value of the 8th term of the 13th row of Pascal's triangle.

43. Graphing Calculator Enter the binomial probability formula as shown. Set the window and table shown. (To get integer values of x, you may need to adjust your window.)

    
    Image Long Description

    1. Examine the graph of y =   7 C x ( 0.5 ) x ( 0.5 ) 7 − x . y equals , sub 7 , cap c sub x . open 0.5 close to the x . open 0.5 close super 7 minus x end super . .  Describe any symmetry in the graph.
    2. Verify the symmetry by displaying values of the function in table form.
    3. Change the graph to y =   7 C x ( 0.6 ) x ( 0.4 ) 7 − x . y equals , sub 7 , cap c sub x . open 0.6 close to the x . open 0.4 close super 7 minus x end super . .  Does this graph have any symmetry? Explain.

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