Twenty five individuals are randomly selected out of 100 shoppers leaving a local bedding store. Each shopper was asked if they
made a purchase during their visit. Each of the shoppers has the same probability of answering ‘yes’ to having made a purchase. The probability that exactly four of the twenty-five shoppers made a purchase could best be found by
1 answer:
we have 25 individuals that are randomly selected out of 100 shoppers leaving a local bedding store, and we know that each of the shoppers has the SAME probability of answering yes to having made a purchase, so we can assume that the probability that a person or a shopper made a purchase is 1 / 12.
Also we know that we selected 25 individuals, so there are 25 shoppers that can say yes, that means our sample size N is 25.
and you want to know the probability that exactly 4 of the 25 shoppers made a purchase
this is a binomial distribution because we can see that we have a sample size n = 25, we have a proportion of success, 1/2to say yes to having made a purchase and we can say that each shopper is independently from the other shoppers.
So the binomial equation is given by: (check the attached image)
so we know that we want P(X=4) because we want to know exactly 4 out of 25.
so n is 25, p is 1/2 and x is 4 so substituting the values into the equation we will get:
P(X=4) = 25C4 * (1/2)^4 * (1 - 1/2)^(25-4)
P(X=4) = 12650 * 0.0625 * 0.000000476
P(X=4) = 0.000377
the probability that exactly 4 of the 25 shoppers made a purchase is....0.00010243
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Answer:
Tina would save the same amount using either option after 20 months.
With either option, Tina would save $700.
Step-by-step explanation:
This problem can be modeled by a first order equation:
Where Tina's saved money after n months is:
S(n) = S(0) + rn, where S(0) is the money put away initially and r is how much she saves every month.
The first option is to put $500 away initially and save $10 every month, so:
The second option is to put $100 away initially and save $30 every month, so:
After how many months would Tina save the same amount using either option?
It will happen at the month n in which , so:
500 + 10n = 100 + 30n
500 - 100 = 30 - 10n
400 = 20n
20n = 400
n = 20.
Tina would save the same amount using either option after 20 months.
How much would she save with either option?
We can choose or
, since they are equal
With either option, Tina would save $700.