• Mar 8th 2013, 12:45 PM
fjtil
Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.

What is the probability that fewer than 40 batteries will last at least 8 hours?
A. 0.7986
B. 0.9211
C. 0.9598
D. 0.0789

In a history class, students take a weekly multiple choice quiz consisting of 6 questions, each with 4 possible answers. If a student randomly guesses at the answer to each question for every quiz, then what is the mean number of correct answers the student will get on each quiz?

Round your answer to one decimal place as necessary. For example, 4.5 would be a legitimate entry.

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

https://edge.apus.edu/cgi-bin/latex....ne%20A_%7B1%7D = chocolate chosen
https://edge.apus.edu/cgi-bin/latex....ne%20A_%7B2%7D = strawberry chosen
https://edge.apus.edu/cgi-bin/latex....ne%20A_%7B3%7D = vanilla chosen
https://edge.apus.edu/cgi-bin/latex.cgi?\inline%20B = ice cream on a cone
https://edge.apus.edu/cgi-bin/latex....Cbar%7BB%7D%3Dice cream in a cup

Find the probability that the ice cream was strawberry flavor, given that it was sold in a cup. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.
• Mar 8th 2013, 03:32 PM
Jame
Hello. The first two problems involve random variables. Specifically, binominal random variable.

Let $X$= "number of batteries that last 8 hours or more"

We want to find $P(X<=39)$.

This sum of all the probabilities of the random variable $X$ from 0 to 39.

What is $P(X=0)$? The probability that no battery lasts?
How about $P(X=1)$?

Once you figure these out you should be able to see what $P(X=i)$ is.

You'll want to calculate $\sum_{i=0}^{39} P(X=i)$

As for the second question: If we let Y = "number of questions correct on the quiz", they are asking you to calculate the mean or expected value of the random variable

Expected value is a weighted average, equal to the sum of the product of the values the RV takes on times the probability it takes on that specific value.
i.e. $\sum P(Y=i)*i$

What values can the random variable $Y$ take on?
What is the probability the student gets exactly 1 question right, i.e $P(Y=1)$?
What is the probability the student gets exactly $i$ questions right, i.e $P(Y=i)$?