Y i ,i = 1,..., n , are i.i.d. Bernoulli random variables with p = 0.4. Let 11eb817c_7712_7c3e_84e6_9150f9e30261_SM2685_11 denote the sample mean. a. Use the central limit to compute approximations for i. Pr( 11eb817c_7712_7c3f_84e6_9fc1aee5d5fd_SM2685_11 0.43) when n = 100. ii. Pr( 11eb817c_7712_7c40_84e6_fff32aba9919_SM2685_11 0.37) when n = 400. b. How large would n need to be to ensure that Pr(0.39 11eb817c_7712_7c41_84e6_1d47bd9e05fa_SM2685_11 0.41) 0.95 (Use the central limit theorem to compute an approximate answer.)

Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Edition 3ISBN: 978-9352863501

Edition 3ISBN: 978-9352863501

Exercise 35

Y i ,i = 1,..., n , are i.i.d. Bernoulli random variables with p = 0.4. Let

denote the sample mean.
a. Use the central limit to compute approximations for
i. Pr(

0.43) when n = 100.
ii. Pr(

0.37) when n = 400.
b. How large would n need to be to ensure that Pr(0.39

0.41) 0.95 (Use the central limit theorem to compute an approximate answer.)

Explanation

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It is provided that
are i.i.d. Bernou...