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

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )

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