Binomial and Normal Probability Problem Set 1 Find the following probabilities: (A) Events A and B a

Binomial and Normal Probability Problem Set

1 Find the following probabilities:

(A) Events A and B are mutually exclusive events defined on
a common sample space If P (A) = 04 and P(A or B) = 065, find P(B)

(B) Events A and B are defined on a common sample space If
P(A) = 030, P(B) = 050, and P(A or B) = 060, find P(A and B)

2 A bag of jelly belly candies contains the following
colored jelly beans: red (5), blue (2), orange (5), brown (21), green (10), and
yellow (6) Construct the probability distribution for x

3 Find the mean and standard deviation of the following
probability distribution:

x 1 2 3

P(x) 02 06 02

4 Classify the following as discrete or continuous random
variables

(A) The number of people in India

(B) The number of planets in the universe

(C) The blood pressures of patients admitted to a hospital
in one day

(D) The length of a centipede

5 In testing a new drug, researchers found that 1% of all
patients using it will have a mild side effect A random sample of 12 patients
using the drug is selected Find the probability that:

(A) exactly one will have this mild side effect

(B) at least one will have this mild side effect

6 X has a normal distribution with a mean of 700 and a
standard deviation of 30 Find the following probabilities:

(A) P(x

(B) P(680

(C) P(x>730)

7 Find the value of z such that 25% of the distribution
lies between it and the mean

8 Assume that the average annual salary for a worker in the
United States is $41,000 and that the annual salaries for Americans are
normally distributed with a standard deviation equal to $7,000 Find the
following:

(A) What percentage of Americans earn below $27,000?

(B) What percentage of Americans earn above $43,000?