1. Use the normal distribution to approximate the desired probability. A coin is

Question

1. Use the normal distribution to approximate the desired probability. A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 13 tosses. What is the probability of being correct 13 or more times by guessing?

ANSWER OPTIONS: A)13.17762% B)13.01096% C) 13.47762% D) 13.37762% E) 13.42762% F) 12.67762%

2. Use the normal distribution to approximate the desired probability. Find the probability that in 210 tosses of a fair die, we will obtain exactly 31 twos.

ANSWER OPTIONS: A) 5.611329% B)6.211329% C) 6.111329% D) 6.161329% E) 5.161329% F)5.211329%

Explanation / Answer

(1) n = 20, p = q = 1/2

= np = 10 and = (npq) = (20 * 1/2 * 1/2) = 2.24

x = 12.5

z = (x - )/ = (12.5 - 10)/2.24 = 1.1161

P(x 13) = P(z > 1.1161) = 0.1322

Answer: 13.22% [Closest answer is option (A)]

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