Question

1. A psychologist believes that 80% of male drivers, when lost, continue to drive, hoping to find the location they seek rather than ask directions. To examine this belief, he took a random sample of 360 male drivers and asked each what they did when lost. If the belief is true, what is the probability that less than 75% said they continue driving?

2. Refer to question 1. For a sample of 320 male drivers, what is the interquartile range for the sample proportion?

Answer 1

1)

p = 0.8

p' = 0.75

z = (p'-p)/sqrt(p(1-p)/n)

z = (0.75-0.80)/ sqrt(0.8*0.2/360)

z = -2.37

P(less than 75% continue driving) = P(z< -2.37) = 0.0089

2)

For interquartile range

probability => 0.25 to 0.75

when probability = 0.25, z = -0.675

thus, -0.675 = (p'-0.8)/sqrt(0.8*0.2/320)

p' = 0.8 - 0.015 = 0.785

Thus, number of drivers = 320*0.785 = 315

when probability = 0.75, z = +0.675

thus, 0.675 = (p'-0.8)/sqrt(0.8*0.2/320)

p' = 0.8 + 0.015 = 0.815

Thus, number of drivers = 320*0.815 = 325

interquartile range is 315 to 325