Angelita and Cynthia like to play a video game against each other that is scored by round. The goal is to score as many points a
s possible in each round. Here are summary statistics how many points they each score per round:
Mean Standard deviation
Angelita \mu_A=900μ
A
=900mu, start subscript, A, end subscript, equals, 900 \sigma_A=96σ
A
=96sigma, start subscript, A, end subscript, equals, 96
Cynthia \mu_C=800μ
C
=800mu, start subscript, C, end subscript, equals, 800 \sigma_C=72σ
C
=72sigma, start subscript, C, end subscript, equals, 72
Both distributions are approximately normal. Suppose we choose a round at random and calculate the difference between their scores. We can assume that their scores each round are independent.
Find the probability that Angelita's score is higher than Cynthia's.
You may round your answer to two decimal places.
P\left(\text{Angelita higher}\right)\approxP(Angelita higher)≈
