Carleen has 104 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 8 kids on her block. Wr
2 answers:
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Answer:
Maximum number of long sleeved shirt that can be purchase is, 8
and
Minimum number of long sleeved shirt that can be purchased is, 0
Step-by-step explanation:
let y represents the number of short sleeves and x represents the number of long sleeves.
As per the given condition:
Members of a school club are buying matching shirts. They know at least 25 members will get a shirt.
we have;
or
....[1]
Since, long sleeves shirt are $ 10 each and short sleeves shirt are $ 5 each.
then;
Total cost of long sleeves is 10x and
the total cost of short sleeves is 5y
Also; the club can spend no more than $ 165
then;
or
......[2]
Solving the inequality equation with the graph :
Plot equation [1] and [2]; we get the maximum at point (8 , 17)
so, x= 8.
If we take minimum value of x =0 then y is between 25 and 33.
so, the solution area is between the lines to the left of where the lines intersect.
Therefore, the maximum number of long sleeved shirts can be purchased is 8 and the minimum number of long sleeved shirt can be purchased is 0
Answer:
8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears
Step-by-step explanation:
For each account, there are only two possible outcomes. Either they are at least 1 month in arrears, or they are not. The probability of an account being at least 1 month in arrears is independent from other accounts. So the binomial probability distribution is used to solve this question.
However, we are working with a large sample. So i am going to aproximate this binomial distribution to the normal.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the probability that fewer than 82 accounts in the sample were at least 1 month in arrears
This probability is the pvalue of Z when X = 82. So
has a pvalue of 0.0885.
8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears