Question

Empirical research on stock market data for two consecutive trading days indicates that 50% of the stocks that went up on the first day also went up on the second day. Yesterday, 400 stocks went up. a. Find the mean of p, where p gives the proportion of the 400 stocks that went up yesterday that will go up today. b. Find the standard deviation of p. c. Compute an approximation for P p <0.54), which is the probability that fewer than 54% of the stocks that went up yesterday will go up again today. Round your answer to four decimal places. (If necessary, consult a list of formulas.) х

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