Exam 8: Probability Distributions and Statistics

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. Round your answer to four decimal places, if necessary. P ( - 1.33 < Z < 1.76 ) = __________

The probability that a videodisc player produced by one microelectronic company is defective is estimated to be 0.03. If a sample of five sets is selected at random, what is the probability that the sample contains no defectives ? At most two defectives ?

The rates paid by 30 financial institutions on a certain day for money market deposit accounts are shown in the accompanying table. Let the random variable X denote the interest paid by a randomly chosen financial institution on its money market deposit accounts and find the probability distribution associated with these data.

Use the formula to determine the probability to four decimal places of the given event. The probability of at least three successes in eight trials of a binomial experiment in which

The odds against an event E occurring are 4 to 1. What is the probability of E not occurring?

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

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​ Colorado Mining and Mineral has 800 employees engaged in its mining operations. It has been estimated that the probability of a worker meeting with an accident during a 1-year period is .1. What is the probability that more than 100 workers will meet with an accident during the 1-year period? ​ Round your answer to four decimal places, if necessary. ​ The probability is __________.

Use the appropriate normal distribution to approximate the resulting binomial distribution. A basketball player has a 75% chance of making a free throw. What is the probability of her making 80 or more free throws in 120 trials?

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. ​ X = The number of hours a child watches television on a given day ​

The tread lives of the Super Titan radial tires under normal driving conditions are normally distributed with a mean of 60,000 mi and a standard deviation of 4,000 mi. ​ If four new tires are installed in a car and they experience even wear, determine the probability that all four tires still have useful tread lives after 55,200 mi of driving. ​

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​ The manager of Madison Finance Company has estimated that, because of a recession year, 5% of its 400 loan accounts will be delinquent. If the manager's estimate is correct, what is the probability that 27 or more of the accounts will be delinquent? ​ Round your answer to four decimal places, if necessary. ​ The probability is __________.

A woman purchased a $10,000, 1-year term-life insurance policy for $150. Assuming that the probability that she will live another year is 0.991, find the company's expected gain. E = $ __________

Use the formula to determine the probability of the given event. Round the answer to four decimal places, if necessary. The probability of exactly no successes in three trials of a binomial experiment in which p = The probability is __________.

A die is cast repeatedly until a 4 falls uppermost. Let the random variable X denote the number of times the die is cast. What are the values that X may assume? ​

Find for the given values of n, x, and p. Round the answer to four decimal places, if necessary. n = 8, x = 4, p = = __________

In a lottery, 6,000 tickets are sold for $1 each. One first prize of $3,000, 1 second prize of $1,200, 3 third prizes of $180, and 10 consolation prizes of $30 are to be awarded. What are the expected net earnings of a person who buys one ticket? $ __________

The tread lives of the Super Titan radial tires under normal driving conditions are normally distributed with a mean of 50,000 mi and a standard deviation of 4,000 mi. ​ Round your answer to four decimal places, if necessary. ​ What is the probability that a tire selected at random will have a tread life of more than 45,200 mi? ​ __________ ​ If four new tires are installed in a car and they experience even wear, determine the probability that all four tires still have useful tread lives after 45,200 mi of driving. ​ __________

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. Round your answer to four decimal places, if necessary. P ( 0.5 < Z < 1.85 ) = __________

A fair die is cast seven times. Calculate the probability of obtaining exactly three 6's. Round the answer to the nearest thousandth.

According to the data released by the Chamber of Commerce of a certain city, the weekly wages of factory workers are normally distributed with a mean of $600 and a standard deviation of $50. What is the probability that a worker selected at random from the city makes a weekly wage of more than $755. ​