Question

A study determined that 19% of a population use a certain brand of laundry detergent. What is the probability that more than 2 shoppers selected at random from 15 shoppers use that brand of detergent?

Answer 1

The binomial distribution applies to this problem. The first step is to work out the probabilities of 0, 1 and 2 of the 15 shoppers use that brand of detergent. Can you do this?

Answer 2

can you help me with this process?

Answer 3

\[P(0\ shoppers)=\left(\begin{matrix}15 \\ 0\end{matrix}\right)0.17^{0}(1-0.17)^{15}=0.83^{15}\]
\[P(1\ shopper)=\left(\begin{matrix}15 \\ 1\end{matrix}\right)0.17^{1}(1-0.17)^{14}=15\times 0.17\times 0.83^{14}\]
\[P(2\ shoppers)=\left(\begin{matrix}15 \\ 2\end{matrix}\right)0.17^{2}(1-0.17)^{13}=\frac{15\times 14}{2}\times 0.17^{2}\times 0.83^{13}\]
We you have worked out the probabilities of 0, 1 and 2 shoppers add the 3 values of probability together.

Answer 4

After finding the sum of the probabilities of zero, one and two shoppers using the brand, subtract this total from 1.00 to find the probability of more than two shoppers out of the fifteen using the brand.

Answer 5

What is the sum of the probabilities of zero, one and two shoppers? im not quite sure if i did this correctly.

Answer 6

What did you get for each of the three probabilities?

Answer 7

P( 0 shoppers)= 2713284.419
P(1 shopper)= 2545311.967
P(2 shoppers)= 0.26921691464

Answer 8

\[P(0\ shoppers)=0.83^{15}=0.061118316\]
\[P(1\ shopper)=15\times 0.17\times 0.83^{14}=0.187773142\]
\[P(2\ shoppers)=\frac{15\times 14}{2}\times 0.17^{2}\times 0.83^{13}=0.269216914\]
As you can see, you need to recheck your first two calculations.

Answer 9

the answer i got from summing up the three probabilities is: 0.518108372 and now i must subtract that by 1.00 so the answer i got from doing so was: 0.481891628 but i think this is incorrect..

Answer 10

Why do you think this answer is incorrect? Do you have a supplied answer?

Answer 11

because when i enter it in it says that it is incorrect.

Answer 12

I am confident that the answer is correct. Possibly the problem relates to how the answer is rounded. For example 0.48 or 0.482 might be expected.