# 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) = 0.4 and P(A or B) = 0.65, find P(B).

(B) Events A and B are defined on a common sample space. If P(A) = 0.30, P(B) = 0.50, and P(A or B) = 0.60, 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) 0.2 0.6 0.2

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 70.0 and a standard deviation of 3.0. Find the following probabilities:

(A) P(x < 68.0)

(B) P(68.0 < x < 72.0)

(C) P(x>73.0)

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?

https://brainmass.com/statistics/probability/binomial-and-normal-probability-problem-set-294603

#### Solution Summary

The solution provides step by step method for the calculation of binomial and normal probabilities. Formula for the calculation and interpretations of the results are also included.

Statistical Problems

1.) Listed below is the percent increase in sales for the MG Corporation over the last 5 years. Determine the geometric mean percent increase in sales over the period. (See attached)

2.) In 1996 a total of 14,968,000 taxpayers in the United States filed their individual tax returns electronically. By the year 2002 the number increased to 46,282,200. What is the geometric mean annual increase for the period?

3.) The events X and Y are mutually exclusive. Suppose P(X) = .05 and P(Y) = .02. What is the probability of either X or Y occurring? What is the probability that neither X nor Y will happen?

4.) A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two hours, find:

a. The probability of making exactly four sales.

b. The probability of making no sales.

c. The probability of making exactly two sales.

d. The mean number of sales in the two-hour period.

5.) In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?

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