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 21 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing?

ANSWER OPTIONS: A) 10.07151% B) 9.071514% C) 9.521514% D) 9.721514% E) 9.871514% F) 9.421514%

2. Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 21.0 percent of the respondents. Estimate the probability that among the next 146 responses there will be at most 42 correct answers.

ANSWER OPTIONS: A) 98.89305% B) 99.19305% C) 99.04305% D) 99.54305% E) 99.49305% F) 99.39305%

Explanation / Answer

1) here, p =0.5 , q = 0.5 , n =21

Mean = n*p = 10.5

Sigma = sqrt(n * p * q)

= sqrt ( 21 * 0.5 * 0.5)

= 2.29

Now, X = 14

By using cental limit theorem,

Z = (x - mean )/ sigma

= (14 - 10.5) / 2.29

= 1.528

we need to find P(Z>z) , by using z standard right tail we get,

P(Z > 1.528 ) = 0.0632

2)

here, p =0.21 , q = 1- p = 1 - 0.21= 0.79 , n =146

Mean = n*p = 146 * 0.21 = 30.66

Sigma = sqrt(n * p * q)

= sqrt ( 146 * 0.21 * 0.79)

= 4.92

Now, X = 42

By using cental limit theorem,

Z = (x - mean )/ sigma

= (42 - 30.66) / 4.92

= 2.30

we need to find P(Z<z) , by using z standard right tail we get,

P(Z < 1.528 ) = 0.9894 = 98.94%

Answer is Option A)

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