Please show ALL work!
1. Find the following probabilities:
a.Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.4 and P(A or B) = 0.9, find P(B).
b.Events A and B are defined on a common sample space. If P(A) = 0.20, P(B) = 0.40, and P(A or B) = 0.56, find P(A and B)
2.Classify the following as discrete or continuous random variables
a.The weight of bags of apples, with 20 apples in a bag
b.The number of times required for a modem to dial an internet provider before connecting
c.A pair of dice is rolled, and the sum to appear on the dice is recorded
d.The time it takes to complete an exercise session.
3.A small bag of Skittles candies has the following assortment: red (10), blue (2), orange (5), brown (21), green (0), and yellow (18). Construct the probability distribution for x.
4.Find the mean and standard deviation of the following probability distribution:
X 1 2 3
P(x) 0.3 0.5 0.2
5.In testing a new drug, researchers found that 5% of all patients using it will have a mild side effect. A random sample of 11 patients using the drug is selected. Find the probability that:
a)exactly two will have this mild side effect
b)at least one will have this mild side effect.
6.A large shipment of TV sets is accepted upon delivery if an inspection of ten randomly selected TV sets yields no more than one defective TV.
a) Find the probability that this shipment is accepted if 5% of the total shipment is defective.
b)Find the probability that this shipment is not accepted if 10% of this shipment is defective
7.X has a normal distribution with a mean of 75.0 and a standard deviation of 2.5. Find the following probabilities:
a)P(x < 70.0)
b)P(72.5 < x < 80.0)
8.Find the value of z such that 40% of the distribution lies between it and the mean.
9.Assume that the average annual salary for a worker in the United States is $27500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6250. Find the following:
a) What percentage of Americans earn below $18000?
b) What percentage of Americans earn above $40000?
P(B) = 0.5
P(A intersection B) = ...
Solutions to problems involving normal distribution, poisson distribution, finding expected value of mean and standard deviation, and finding probability values under normal distributions are explained with step by step explanation in the attached solution file. For the problems solved in the attached file, please see the specific problems.