Ali and Bruno both run the 400 meter dash for their track team. Their coach frequently records their finishing times (in seconds
), which are summarized in the table below.
Mean Standard deviation
Ali \mu_A=59μ
A
=59mu, start subscript, A, end subscript, equals, 59 \sigma_A=4.8σ
A
=4.8sigma, start subscript, A, end subscript, equals, 4, point, 8
Bruno \mu_B=50μ
B
=50mu, start subscript, B, end subscript, equals, 50 \sigma_B=3.6σ
B
=3.6sigma, start subscript, B, end subscript, equals, 3, point, 6
Both distributions are approximately normal. Suppose we choose a random 400 meter race and calculate the difference between their times. It's reasonable to assume that their times are independent.
Find the probability that the Ali's finishing time is faster than Bruno's.
You may round your answer to two decimal places.
P\left(\text{Ali faster}\right)\approx
