Question

Suppose only 75% of all drivers in a certain state regularly wear aseat belt. A random sample of 500 drivers is selected. What is theprobability that
a). Between 360 and 400 (inclusive) of the drivers in the sampleregularly wear a seat belt?
b). Fewer than 400 of those in the sample regularly wear a seatbelt?

Part b)is what I am having a hard time with. This is what I did for part a).
using a Normal approximation:
z = (400.5-500*0.75) /
sqrt(500*0.75*0.25) = 2.63

z = (359.5-500*0.75) /
sqrt(500*0.75*0.25) = -1.60

these numbers correspond to areas of 0.9957 and 0.0548, so the probability is: 0.9957-0.0548 = 0.9409

I need help solving part b).

Answer 1

Use the same method you did for part a. Only now you are dealing with just an exclusive upper-bound. Just make sure you use the right correction factor and you should be set.

Answer 2

Your result from part (a) of P(X=<400) is the same for P(X<400).