Mathematics, 20.07.2019 07:30 Ashbff18

Areport i just made up says that 11% of all flowers sold from a particular flower shop are carnations. if this flower shop sells 316 bouquets on a random day, what is the probability that: a) fewer than 40 are carnations? b) at least 25 are carnations? c) between 25 and 40 are carnations? note: a through c are not answers. they are parts of the question that need to be solved individually.

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This is a problem on a binomial probability distribution. A binomial probability distribution has fixed number of trials, n. In this case, n is equal to 316. Also, the trials in a binomial probability distribution must be independent. Each trial must have all outcomes classified into two categories--carnation or not carnation. Lastly, the probability of success remains the same in all trials.

The binomial probability formula is given by
$p\left(x\right)=C\left(n,\:x\right)p^x\left(q\right)^{n-x}$
where
n=number of trials
x=number of successes among n trials
p=probability of success in any one trial
q=probability of failure in any one trial (q=1-p)

So, from the given problem, the following quantities are given:
n=316

Part A
The probability of obtaining fewer than 40 (0 to 39) carnations is the summation of all the binomial probabilities from 0 to 39. That is
$p\left(x\ \textless \ 40\right)=\sum _{x=0}^{39}\:C\left(316,\:x\right)\left(0.11\right)^x\left(0.89\right)^{316-x}=0.8048$

Part B
The probability that at least 25 are carnations is the sum of binomial probabilities of x from 25 to 316. That is
$p\left(x\ge 25\right)=\sum _{x=25}^{316}\:C\left(316,\:x\right)\left(0.11\right)^x\left(0.89\right)^{316-x}=0.9720$

Part C
The probability that carnations are between 25 and 40 is given by the sum of individual binomial probabilities from 26 and 39. That is
$p\left(26\le x\le 39\right)=\sum _{x=26}^{39}\:C\left(316,\:x\right)\left(0.11\right)^x\left(0.89\right)^{316-x}=0.7615$

Therefore, the probability that there are fewer than 40 carnations is 0.8048, at least 25 carnations is 0.9720, and between 25 and 40 is 0.7615.

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The american colonies would have been ruled by a king.

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One shot. if 60% of 10 is 6, then what is 70%? we know it would be seven (since 60% is mathematically 60/100, or 6/10, then 70% is 70/100, or 7/10) but we can check anyway using ratios: 6 : 60% = x : 70%*inverse multiplicationx * 60% = 6 * 70%*divide both sides by 60%x = (6 * 70%) / 60%x = 7and since he has made 6 shots already, he would need just one more to get 7 shots or 70%. if the explanation is too confusing, comment and i will try to

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