Step by step 6x + 3y = 12
2 answers:
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Answer:
a) sample size ≥ 30
b) 0.0017
Step-by-step explanation:
a) The central limit theorem states that for population with mean μ and standard deviation σ and take sufficiently large random samples from the population. This will hold provided the sample size is sufficiently large (usually n > 30) for a normal population.
Therefore the sample size should be greater or equal to 30 i.e n ≥ 30.
b) Given that n = 45, μ = 11.4 minutes and σ = 3.2 minutes, the z score (z) is given by the equation:
Substituting values to get:
Using the z table:
P(x < 10) = P(z < -2.93) = 0.0017
the probability that a random sample of n=45 oil changes results in a sample mean time of less than 10 minutes is 0.0017
Answer:
0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.
Step-by-step explanation:
Independent events:
If two events are independent, the probability of both happening is the multiplication of their probabilities.
Rock-paper-scissors rules:
A player that choose rocks beats one who chooses scissors.
A player that choose paper beats one who chooses rocks.
A player that choose scissors beats one who chooses paper.
Probability that roommate A wins the game and thus does not have to wash the dishes.
3 possible events:
Roommate A - Rocks(21% of the time) and Roommate B - Scissors(18% of the time)
So
Roommate A - Paper(39% of the time) and Roommate B - Rocks(61% of the time).
So
Roommate A - Scissors(40% of the time) and Roommate B - Paper(21% of the time).
So
Probability of roommate A winning:
0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.