Hello. The first two problems involve random variables. Specifically, binominal random variable.
Let = "number of batteries that last 8 hours or more"
We want to find .
This sum of all the probabilities of the random variable from 0 to 39.
What is ? The probability that no battery lasts?
How about ?
Once you figure these out you should be able to see what is.
You'll want to calculate
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.
What values can the random variable take on?
What is the probability the student gets exactly 1 question right, i.e ?
What is the probability the student gets exactly questions right, i.e ?