Question

A $1 scratch off lotto ticket will be a winner one out of five times. Out of a shipment of

n = 180

lotto tickets, find the probability for the lotto tickets that there are each of the following. (Round your answers to four decimal places.)

(b) somewhere between 53 and 63 prizes


(c) more than 63 prizes

Answer 1

A Loinner one out of five times, 1. l., Ñ = 5 = 0.2 E no 180 cq = 0.8 Here, we need to find the probability that the lotto tickets that these are each of the following i-C., (b) Some where between 53 and 63_prizes: we need to find pl53 < X <63):-? we know that z=x-le de = np = 180 (0.2) = 36 : Le = 36 ) ra impg - V 180 (0-2) (0.8) 6 = 28.8 = 5, 3666 Ti Oo 5.3666)

P (53 exc63) a p(x=46 cz ex-de) - C Z L 53-36 72 63-36 | 5.3666 5.3666 <Z 17 - | 5.3666 27 5.3666 >> P 13.1677 CZ < 5.0311) => P(Z<5.02) - Plz23. 1677) a P (Z2 5.03) - P(Z <3.17) using standard Normal z-table, 5) 0.9999 - 0.9992 3 0.0007 .:P153 < x <63) = 0.0007 (c) more than 63 prizest we need to find P(x>63) = ?

P(X>63) = ? we know that z=X-le P[X363) plz > 63-36 5.3666 > P(Z > 1240) » P(Z > 5.03111) ible using standard Normalz-table Standao >> P(Z >5.03) > 1- P(Z <5:03) a 1-0.99999 => 0.0001 - P(X>63) = 0.0001]