Question

The probability that a person has type U blood is 0.37. A survey of 190 people taken. Let X be the number of people with type U blood. Yoa may use the fact that the mean is 70.3 and the standard deviation (to the nearest thousandth) is 6.655. [12 pts.) a) Use normal approximation to approximate the probability that less than 73 people have type U blood. X0-37 b) Use normal approximation to approximate the probability that exactly 71 people have type U blood.

Answer 1

Given, P type U blood)=P=0.37 - mean = M = 70.3 standard deviation=0=6.655 tet 2= X-M is a standard nommal random variable a) Answer: P(x<73) = P(x2773-0.5). Accmling to normal oppoecimation = P(x< 72.5) = P x < 72.5-70.3) -Tre 6.655. = P(Z <0.33) using 2-table, weget P(x273) = 0.6293

b) Answer: P(X=71) =P(71-0.5<x <7140.5) According to nemal approacimation = P(70.5< X <71.5) -pl 70.5-70.3, X-M, 71.5-70.3 ) =PL6556 .655. = P(0.03 < 260.18) = P(2<0.18 ) -P(Z <0.03) using Z-table, we get = 0.5714-0.5120 P(x=71) = 0.05947