Answer:
a. E(F)=0.875
b. 99.9976%
c. P(X=2)=0.1683
Step-by-step explanation:
a. We notice that this is a binomial distribution with the probability of success;

#We are given the sample size, n=7. The Expected value is calculated as:

Hence the expectation, E(F)=0.875
b. To calculate the probability of the range of F, we need to calculate all possible outcomes of F in the given sample;

Hence, the range of F is 99.9976%
c. The probability that F=2 is calculated using the binomial distribution function as:

Hence, the probability of F=2 is 0.1683