28 At rush hour on a typical day 250 of the cars approaching

2.8. At rush hour on a typical day, 25.0% of the cars approaching a fork in the street turn left and 75.0% turn right. On a particular day, 283 cars turned left and 752 turned right. Find the predicted uncertainty in these numbers and the probability that these measurements were not made on a \'\'typical day\'\'; that is, find the probability of obtaining a result that is as far or farther from the mean than the result measured on the particular day.

Solution

Number of cars approaching a fork in the street turn left = 25%

Number of cars approaching a fork in the street turn right = 75%

On a particular day:

Number of cars turned left = 283

Number of cars turned right = 752

Uncertainty in turning the cars left = 100 - 25

= 75%

= 0.75

Uncertainty in turning the cars right = 100 - 75

= 25%

=0.25

Probability of turning the cars left = 283/(283 + 752)

= 283/1035

= 0.2734

Probability of turning the cars right = 752/(283 + 752)

= 752/1035

= 0.7265