Please read carefully, there are 2 parts to this problem. I have parts a and b f

Question

Please read carefully, there are 2 parts to this problem. I have parts a and b for Part 1, still need parts c and d. Please explain each step.

For part 2: I have b. I still am trying to find parts a, c and d.

Problem Statement:

Part 1: Wishing to test the claim that a certain coin is “fair”: You toss the coin 250 times, and get 140 heads. Using the appropriate Binomial Distribution model for a fair coin, find the following values:

a.) The mean and standard deviation of the sample heads count X, for the 250 tosses. Answer:The mean for 250 tosses is 125 and the standard deviation of the sample heads count x, for 250 tosses is approx. 7.9057%.

b.) The difference d between the heads count X from your test, and the expected heads count. Answer: The difference between the heads count X from the test, and expected heads count is 15.

c.) The percent probability that X would fall at least d away from expected, in the positive direction?

d.) The percent probability that X would fall at least d away from expected, in either direction?

Part 2:

Referring back to the completed coin-toss experiment data in Part 1 above. Using the Central Limit Theorem and the appropriate Normal Distribution Model for a fair coin, find the following values:

I have part b, need part a, c and d.

Explanation / Answer

here n = 250 p = 0.5 , q = 0.5

(X = k) = nCk p^k*q^k = 250Ck (1/2)^250

E(X) = np = 250*0.5 = 125

sd (X) = sqrt(npq) = 7.9057 { note this is 7.9057 and not 7.9057 %)

b) difference = 140 -125 = 15

c) P(X > 140)

= 0.024853393

d) P(X > 140 or X < 110 )

= 2 * P(X > 140) {As distribution is syymetric dut p = 0.5 }

= 2 *0.024853393

= 0.04970

part 2

a) p^ = 0.5

sd(p^ ) =sqrt(p^q^/n) = 0.0316

b) difference = 140/250 -0.5 = 0.06

c) P(p^ > 0.5 + 0.06)

P(p^ > 0.56)

Z = (p^ - 0.5)/0.0316

P(Z > (0.56-0.5)/0.0316)

p(Z> 1.899) =0.0288

d) required probability =2 *0.0288 = 0.0576

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