A sports club needs to raise at least $500 by selling chocolate bars for $2.50 each. Sebastian wants to know how many chocolate
2 answers:
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Answer:
i) A total of 40320 different arrangements
ii) For the initial 3 spots, there are 336 different combinations.
Step-by-step explanation:
Given: The total finalists = 8
The count of boys = 3
The count of girls = 5
To determine the number of sample point in the sample space S for possible arrangements, we calculate the factorial of 8!
The number of possible arrangements equals 8!
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
= 40320
ii) Among the 8 finalists, we must select the first 3 spots. The sequence matters, hence we utilize permutation.
nPr =
Here n = 8 and r = 3
Substituting n = 8 and r = 3 into the formula, we arrive at
8P3 =
=
= 6.7.8
= 336
Thus, there are 336 different arrangements for the first 3 spots.
Answer:
There is a probability of 24.51% that the weight of a bag exceeds the maximum permitted weight of 50 pounds.
Step-by-step explanation:
Problems dealing with normally distributed samples can be addressed using the z-score formula.
For a set with the mean and a standard deviation
, the z-score for a measure X is calculated by
Once the Z-score is determined, we consult the z-score table to find the related p-value for this score. The p-value signifies the likelihood that the measured value is less than X. Since all probabilities total 1, calculating 1 minus the p-value gives us the probability that the measure exceeds X.
For this case
Imagine the weights of passenger bags are normally distributed with a mean of 47.88 pounds and a standard deviation of 3.09 pounds, thus
What probability exists that a bag’s weight will surpass the maximum allowable of 50 pounds?
That translates to
Thus
has a p-value of 0.7549.
Additionally, we have that
There is a probability of 24.51% that the weight of a bag will exceed the maximum allowable weight of 50 pounds.
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