statistics question: It was recently reported that 80% of drivers text message while driving.

Question

Find the APPROXIMATE probability that at most 555 drivers in a sample of 700 drivers text message. 

 

The answer is = 0.3336 i am just not sure how to get this answer. 

Answer 1

80% of 700 = 560

you could use a binomial to approximate the normal, as there are two events, either text or not

mean = np = .80 x 700 = 560

var = npq = 560 x .2 = 112

sd = sqrVar = sqr112 = 10.583

z score for 555 = (555- 560)/sqr112 = about -0.4724555913

use z tables to find the area under the normal curve

= the probability

= .3183= 31.83% = p(x<z)

.3336 is approximately .3183