Olga plans to take a trip from her house in San Marcos, Texas, to a friend's house in Zapata, Texas. She measured the distance between the two
places on a map and found it to be 8 inches. If the scale on the map is
1/2 inch represents 14 miles, determine the actual distance in miles
between the two places.

Step-by-step explanation:

Given ;

a) P ( X = 13 ) = C(15,13) x 0.56^13 x (1-0.56)^2 = 0.0108

b) Mean = np = 15 x 0.56= 8.400

Standard deviation = √(np(1-p)) = √(15 x 0.56 x (1-0.56)) = 1.9225

c) P(X>10) = 1 - P(X≤10) = 1 - 0.8633 = 0.1367

d) P(X≥12) = P(X=12) + P(X=13) + P(X=14) + P(X=15) = 0.0498

e) P(Y=3) = C(3,1) x 0.56^1 x (1-0.56)^2 x 0.56 = 0.1821

f) P(Y=2) = C(2,1) 0.56^1 x (1-0.56)^1 x 0.56 = 0.2760