Question

Given that 57% of all gold dealers believe next year will be a good one to speculate in south afrucan gold coins, in a simple random sample of 150 dealers, what is the probability that between 54% and 63% believe that it will be a good year to speculate? Please show work

Answer 1

Given. Sample size(n)= 150 Proportion (p=0.57 Implies. q=1-p = 1-0.57 = 0.43

The required probability is. 0.54-0.570 - p P(0.54 < p <0.63) = P - 0.57) (0.43) V 150 Vn 0.63 -0.57 (0.57)(0.43) V 150 P 0.54-0.572 0.63 -0.57 <Z < (0.57)(0.43) (0.57)(0.43) V 150 V 150 = P(-0.74 <Z <1.48) = P(Z <1.48)-P(Z <-0.74) = 0.9306-0.2297 (Using standard normal table) = 0.7009