I am preparing for a chapter test in my prob/stat class and since my teacher no longer cares about our class and the textbook is as confusing as a foriegn languaga, i am in need of help. i am trying to review an old quiz ao here is one of the questions.
the probability that a costomer selects 1,2,3,4 or 5 items at a convenience store are 3.02,.012,.023,.018 and.015, respectively.
find P(X>3.5)
find P(X<5)
I think there's a mistake with the probabilities were given. 1) probabilities can't be >1 (you get greater than 100% chance). 2) the probabilities don't add up to 1
here is what I think they should be:
.32, .12, .23, .18, .15
P(x>3.5) = probability that a customer selects more than 3.5 items = p(4) + p(5) = .18 + .15
you can do the other one by yourself.
23
To find the probabilities P(X > 3.5) and P(X < 5) in this scenario, you need to use the information given about the probabilities of selecting different numbers of items at the convenience store.
To find P(X > 3.5), you want to determine the probability of a customer selecting more than 3.5 items at the store. Since the number of items is discrete, you will sum the probabilities of selecting 4 or 5 items.
Here's how you can calculate P(X > 3.5):
1. Identify the probabilities for selecting 4 and 5 items separately.
- P(X = 4) = 0.018
- P(X = 5) = 0.015
2. Add these probabilities to find the cumulative probability of selecting more than 3.5 items:
- P(X > 3.5) = P(X = 4) + P(X = 5) = 0.018 + 0.015 = 0.033
Therefore, the probability of a customer selecting more than 3.5 items at the convenience store is 0.033.
To find P(X < 5), you want to determine the probability of a customer selecting less than 5 items at the store. Again, you will sum the probabilities of selecting 1, 2, 3, and 4 items.
Here's how you can calculate P(X < 5):
1. Identify the probabilities for selecting 1, 2, 3, and 4 items separately.
- P(X = 1) = 0.302
- P(X = 2) = 0.012
- P(X = 3) = 0.023
- P(X = 4) = 0.018
2. Add these probabilities to find the cumulative probability of selecting less than 5 items:
- P(X < 5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.302 + 0.012 + 0.023 + 0.018 = 0.355
Therefore, the probability of a customer selecting less than 5 items at the convenience store is 0.355.
Remember to double-check your calculations and ensure that the given probabilities are accurate before using them in your test preparation.