1. Using the normal-curve approximation find the porbability of getting 5 heads

Question

1. Using the normal-curve approximation find the porbability of getting 5 heads and 7 tails in 12 flips of a blanced coined.

7.2 Suppose that a continuous random variable takes on values on values on the interval fr t 0 to 4 and that the graph of its probability density is given by the blue tr to e line Figure 7.19. (a) Verify that the total area under the curve is equal to 1. (b) What is the probability that this random variable will take on a val ue than 3? (c) What is the probability that this random variable will take on a value betwe 1 and 2? Figure 7.18 Diagram for Exercise f(x)-1 4 4 Figure 7.19 Diagram for Exercise 7.2. f(x)- 4

Explanation / Answer

Question 7.2:

a) The area under the PDF is computed as:

= Area of the rectange with height of 1/4 = 0.25 and width of (5-1),

= (5-1)*0.25 = 4*0.25 = 1

Therefore verfied that the area under the curve is 1.

b) Probability that the variable takes on a value less than 3 is computed as:

= Area of the rectange with height of 1/4 = 0.25 and width of (3-1),

= (3-1)*0.25

= 2*0.25

= 0.5

Therefore 0.5 is the required probability here.

c) Probability that it takes on value between 1 and 2 is computed as:

= Area of the rectange with height of 1/4 = 0.25 and width of (2-1),

= (2-1)*0.25

= 0.25

Therefore 0.25 is the required probability here.

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