Exam 8: Probability Distributions and Statistics

A probability distribution has a mean of 60 and a standard deviation of 1.5. Use Chebychev's inequality to find the value of c that guarantees that the probability is at least 75% that an outcome of the experiment lies between 60 - c and 60 + c. c = __________

Let Z be the standard normal variable. Round your answers to two decimal places. ​ Find the value of z if z satisfies: ​ __________ ​ Find the value of z if z satisfies: ​ __________

The probability distribution of a random variable X is Compute the mean, variance, and standard deviation of X. Round your answers to the nearest hundredth, if necessary. __________ Var (X) = __________ __________

The daily earnings X of an employee who works on a commission basis are given by the following probability distribution. Find the employee's expected earnings. Give your answer to the nearest cent. E (X) = $ __________

The scores on an Economics examination are normally distributed with a mean of 74 and a standard deviation of 11. If the instructor assigns a grade of A to 10% of the class, what is the lowest score (rounded to the nearest integer) a student may have and still obtain an A?

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. P ( - 1.36 < Z < 1.75 )

Maria sees the growth of her business for the upcoming year as being tied to the gross domestic product (GDP). She believes that her business will grow (or contract) at the rate of 5%, 4.5%, 3%, 0%, or - 0.5% per year if the GDP grows (or contracts) at the rate of between 2 and 2.5%, between 1.5 and 2%, between 1 and 1.5%, between 0 and 1%, and between - 1 and 0%, respectively. Maria has decided to assign a probability of 0.11, 0.23, 0.43, 0.19, and 0.04, respectively, to each outcome. At what rate does Maria expect her business to grow next year? Give your answer to three decimal places, if necessary. __________ %

The probability distribution of the random variable X is shown in the accompanying table. Find the following, rounded to two decimal places if necessary. __________ __________ __________

Steffi feels that the odds in favor of her winning her tennis match tomorrow are 2 to 10. What is the (subjective) probability that she will win her match tomorrow?

The weights, in ounces, of ten packages of potato chips are given. Find the average of these weights. __________ oz. Find the mode of these weights. __________ oz. Find the median of these weights. __________ oz.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of a histogram associated with a probability distribution is a number between 0 and 1.

The expected lifetime of the deluxe model hair dryer produced by Roland Electric has a mean life of 21 mo and a standard deviation of 4 mo. Find the probability that one of these hair dryers will last between 16 and 26 mo. Give your answer as a fraction.

A new drug has been found to be effective in treating 50% of the people afflicted by a certain disease. If the drug is administered to 800 people who have this disease, what is the standard deviation of the number of people for whom the drug can be expected to be effective?

The following table gives the scores of 30 students in a mathematics examination. Find the mean and the standard deviation of the distribution of the given data. Hint: Assume that all scores lying within a group interval take the midvalue of that group.

Find the expected value of a random variable X having the following probability distribution:

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. P ( Z > 1.14 )

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. P ( 0.3 < Z < 1.85 )

A probability distribution has a mean of 45 and a standard deviation of 1. Use Chebychev's inequality to estimate the probability that an outcome of the experiment lies between 43 and 47.

The histograms represent the probability distributions of the random variables X and Y. Determine by inspection which probability distribution has the larger variance. Answer a or b.

In a lottery, 4,000 tickets are sold for $1 each. One first prize of $2,000, 1 second prize of $800, 3 third prizes of $120, and 10 consolation prizes of $12 are to be awarded. What are the expected net earnings of a person who buys one ticket?