Problem 6 10 points A psychologist believes that 80 of male

Problem 6. (10 points) A psychologist believes that 80% of male drivers when lost continue to drive, hoping to find the location they seek rather than ask for direction. To examine this belief, he took a random sample of 400 male drivers and asked each what they did when lost. If the belief is true, determine the probability that less than 75% said they continue driving?

Solution

75% of 400 is 0.75*400 = 300.

We first get the z score for the critical value:          
          
x = critical value =    300      
u = mean = np =    320      
          
s = standard deviation = sqrt(np(1-p)) =    8      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -2.5      
          
Thus, the left tailed area is          
          
P(z <   -2.5   ) =    0.006209665 [ANSWER]