"The random variable X has a binomial distribution with parameters n=100 and p=0.8. Find the mean and the variance of X."
"A manufacturing process produces components which are free from any faults with probability p. Find the probability that in a sample of size 50 from a large batch there are fewer than 4 faulty components when p = 0.95. Find the probability that in a sample of size 50 there are fewer than 10 faulty when p = 0.75."
"Use the table to give a suitable approximation to the probability that 𝑋 ≥ 5 where X is binomial random variable with parameters p = 0.05 and n = 400."
"Which of the following is not a requirement of a binomial distribution?
a. Constant probability of success
b. Only two possible Bernoulli outcomes
c. Fixed number of trials
d. Equally likely outcomes"
"Determine whether the distribution is a discrete probability distribution.
X 0 1 2 3 4
P(x) 0.2 0.2 0.2 0.2 0.2"
"Is the distribution a discrete probability distribution?
A. No, because each probability is not between 0 and 1, inclusive.
B. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1 comma inclusive.
C. Yes, because the sum of the probabilities is equal to 1.
D. No, because the sum of the probabilities is not equal to 1"
"An insurance company sells insurance policies. Each insurance policy leads to claims with an expected value of $100 and a standard deviation of $3,000.The number of policies sold is normally distributed with a mean of 1,000 and a standard deviation of 150.
(a) What is the expectation of the total of all the claims from policies sold by this company?
(b) What is the variance of the total of all the claims from this company's policies?"
"A probability distribution of the number of overtime hours worked in one week per employee is listed below.