The probability of you being the leadoff hitter is <span>8.3%.</span>
Explanation:
The number of possible rosters can be calculated with permutations, knowing that the coach can choose the first hitter among all 12 players, then the second hitter among the 11 players remaining and so on until the 9th hitter among the remaining 4 players.
Therefore:
Possible rosters = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 = 79833600
The leadoff hitter is the first player in the batting order, therefore the number of possible rosters in which you are chosen as the first one is:
You leadoff = 1 <span>× 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 = 6652800
The probability of you being leadoff is:
P</span> = You leadoff / <span>Possible rosters
</span> = 6652800 / 79833600
= 1 / 12
= 0.08333
= 8.3%
Note that this is exactly the probability of you being chosen out of the 12 players of the team in a one-pick choice because it does not matter how the rest of the batting order is composed.
Answer:
n = 14
Step-by-step explanation:
7n +9 = -1+6(n+4)
Distribute
7n+9 = -1 +6n+24
Combine like terms
7n +9 = 6n +23
Subtract 6n from each side
7n -6n+9 = 6n-6n +23
n+9 = 23
Subtract 9 from each side
n+9-9=23-9
n = 14
Answer:
The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion 
(if no previous estimate use 0.5) and M is the desired margin of error.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of 
.
The margin of error is of:
95% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
Needed sample size:
The needed sample size is n. We have that:
The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion (if no previous estimate use 0.5) and M is the desired margin of error.
