Question

Empirical research on stock market data for two consecutive trading days indicates that 40 % of the stocks that went up on the first day also went up on the second day. Yesterday, 600 stocks went up. a. Find the mean of p, where p gives the proportion of the 600 stocks that went up yesterday that will go up today. b. Find the standard deviation of p. c. Compute an approximation for P (p<0.37), which is the probability that fewer than 37% 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.) ? X a. b. C.

Answer 1

Given that, population proportion (p) = 0.40

Sample size (n) = 600

a) mean of sample proportion $(\hat p)$ is,

μρ = p = 0.40 => μρ = 0.40

b) standard deviation of sample proportion $(\hat p)$ is,

_ p*(1 - p)_ Op = 14 0.40 * (1 – 0.40) 600 2 = 0.02 V => Jp = 0.02

c) We want to find,

P(p < 0.37)

0.37 -0.40 P <0.37) = PP Mp -) = P(Z < -1.5) = 0.0668

=> P p <0.37) = 0.0668