Question

Psychologists estimate that 80% of male drivers, when lost in trying to find a location, continue to drive rather than asking for directions. If this estimate is correct, what is the probability that, in a random sample of 100 lost male drivers, the proportion who continue to drive is

                           a.    at least 0.70?

                           b.    less than 0.85?

Answer 1

(a)

n = 100

p = 0.8

q = 1 - p = 0.2

SE =

=

To find P(0.7):

Z = (0.7 - 0.8)/0.04 = - 2.50

Table of Area Under Standard Normal Curve gives Z = 0.4938

So

P(0.7) = 0.5 - 0.4980 = 0.0020

So,

Answer is:

0.0020

(b)

n = 100

p = 0.8

q = 1 - p = 0.2

SE =

=

To find P( <0.85):

Z = (0.85 - 0.8)/0.04 = 1.25

Table of Area Under Standard Normal Curve gives Z = 0.3944

So

P(<0.85) = 0.5 + 0.3944 = 0.8944

So,

Answer is:

0.8944