Two brothers, Michael and Alan, were in a bowling league that met once a week. From past experiences, it is known that both brothers' scores are
approximately normally distributed where Michael has a mean score of 150
with a standard deviation of 30, and Alan has a mean score of 165 with a
standard deviation of 15. Assuming that their scores are independent, which
of the following values is closest to the probability that Michael will have a
greater core than Alan in a single game?
0.16
0.28
0.31
0.33
0.37

The correct option is;

0.28

Step-by-step explanation:

The given parameters are;

The mean score for Michael, = 150

The standard deviation, σ₁ = 30

The mean score for Alan,   = 165

The standard deviation, σ₂ = 15

Taking n₁ = n₂ = 1

Taking μ₁ - μ₂ = 0

The p-value for a z-score of -0.577 from the z-table is 0.28434

Therefore, the probability that Michael, with mean score, = 150 will have a greater score than Alan, with a mean score of = 165 is 0.28434 ≈ 0.28

Therefore, the correct option is 0.28

468

step-by-step explanation:

step-by-step explanation: