The positions on a lacrosse team are called defenders (D), midfielders (M), and attackers (A). One player is chosen at random to
lead the team in
exercises before each game. The letters MDD mean that a midfielder was chosen at the first game and a defender was chosen at the next two
games. The list of all possible outcomes is shown, where each outcome has equal probability of occurring.
AAA AMA ADA
MAA
MDA DAA DMA DDA
AAM AMM ADM MAM MMM MDM
DMM DDM
AAD AMD ADD MAD MMD MDD DAD DMD DDD
MMA
DAM
What is the probability that a defender is chosen at least once, given that a midfielder is chosen at the first game?
exercises before each game. The letters MDD mean that a midfielder was chosen at the first game and a defender was chosen at the next two
games. The list of all possible outcomes is shown, where each outcome has equal probability of occurring.
AAA AMA ADA
MAA
MDA DAA DMA DDA
AAM AMM ADM MAM MMM MDM
DMM DDM
AAD AMD ADD MAD MMD MDD DAD DMD DDD
MMA
DAM
What is the probability that a defender is chosen at least once, given that a midfielder is chosen at the first game?
1 answer:
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Answer:
The probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
The information provided is:
As the sample size is large, i.e. <em>n</em> = 276 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion.
Compute the value of as follows:
Thus, the probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.