Question

The proportion of left-handed people in the general population is about 0.1. Suppose a random sample of 225 people is observed. Using our 'rule of thumb; can we use normal approximation values for this sampling distribution? Yes + np = 22.5 and ng= (Click to view hint) What is the mean of the sample proportion? др (Click to hide hint) My =P What is the standard error? (Click to view hint) What interval is almost certain (probability 0.997) to contain the sample proportion of left-handed people? The sample proportion is almost certain to be between and (Click to hide hint) Since the Empirical Rule applies, the probability is approximately 0.997 that the sample proportion falls withing 3 standard deviations of the mean. Find 21 = Mp - 360p) and x2 = Mji + 3(0) In a sample of 225 people, would it be unusual to find that 40 people in the sample are left-handed? Yes - (Click to view hint) Find the approximate probability of at least 30 in 225 of being left-handed. What is the sample proportion? P (Round to the nearest hundredth.) (Click to view hint) Write the problem using probability notation. PP = 0.13)
The proportion of left-handed people in the general population is about 0.1. Suppose a random sample of 225 people is observed.

Answer 1

the proportion of left-handed people in the general population is 0.1. A random sample of 225 people is ohserved. We can use normal approximation for this sampling distribution. 0.1 X 225 22.5 and up The mean 0.9 X 225 202.5 ng = the sample proportion will be of the وبلر P 0:1 The standard error will be , E pli-p) 0,1(1-0-1) 225 0.02 n 0.02 p The be, 0.04 99.7% of the confidence interval for the sample proportion of left-handed people will u po - 36 0.1 - 360-02) u ê t the sample proportion is almost certain to be 72 36 p 0-1 + 310.01) 0.16 between 0.04 and 0.16

will be, In a sample of 225 people, the probability that 40 people are left-handed P(x=40) P( 39.5 < x < 40-5) 39.5- (225X0.1) << < 40.5-(225X0.1) J 225 x 0-1x0.9 =p <4) pl 225 X O.1Xo.g - 3.777 <2< 4 1 -1 O that at the appros . the probability is o. Therefore it will be unusual to find that Yo people in the sample are left-handed. We have to find oximate probability least 30 in 225 , are left handed. The sample proportion rtion will be, å - The probability will be calculated as, PL P = 0.13) = PL 2 21.5) - 1 - Plz<1-5) 30 0:13 225 1 - 0.933 0.067 0.067. So the probability is