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Empirical research on stock market data for two consecutive trading days indicates that 50% of the stocks that went up on the
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Answer #1

a) \mu_{\widehat p} = p = 0.50

b) \sigma_{\widehat p} = sqrt(p(1 - p)/n)

          = sqrt((0.5 * 0.5)/400)

          = 0.025

c) P(\widehat p < 0.54)

= P((\widehat p - \mu_{\widehat p} )/\sigma_{\widehat p} < (0.54 - \mu_{\widehat p} )/\sigma_{\widehat p} )

= P(Z < (0.54 - 0.5)/0.025)

= P(Z < 1.6)

= 0.9452

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