Exam 8: Probability Distributions and Statistics

A fair die is cast six times. Calculate the probability of obtaining exactly three 6's. Round the answer to three decimal places, if necessary. ​ The probability is __________.

TKK Products manufactures electric light bulbs in the 50-, 60-, 75-, and 100-watt range. Laboratory tests show that the lives of these light bulbs are normally distributed with a mean of 750 hr and a standard deviation of 60 hr. What is the probability that a TKK light bulb selected at random will burn between 750 and 870 hr?

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​ A fair coin is tossed 20 times. What is the probability of obtaining fewer than 6 heads? ​

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. A game between two persons is fair if the expected value to both persons is zero.

The McCormack Company manufactures solar panels. As a part of its quality control, the company checks the day's production by examining samples of 10. The following table shows the number of defective panels contained in a distribution of 60 samples. Find the mean number of defective panels per sample, and assuming that the distribution is binomial, estimate the percentage of defective solar panels in the day's production. (Round your final anwers upto two decimal places.)

Let Z be the standard normal variable. Find the values of z, rounding to two decimal places, if z satisfies __________ __________

Find to four decimal places for the given values of n, x, and p.

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 0.13, 0.24, 0.39, 0.19, and 0.05, respectively, to each outcome. At what rate does Maria expect her business to grow next year?

The probability that a videodisc player produced by one microelectronic company is defective is estimated to be 0.01. If a sample of twenty sets is selected at random, what is the probability that the sample contains no defectives ? At most two defectives ? Round your answers to three decimal places, if necessary. = __________ = __________

It is estimated that one third of the general population has blood type . If a sample of nine people is selected at random, what is the probability that at most three of them have blood type ?

Suppose that one-fourth of the new buildings in a town are in violation of the building code. If a building inspector inspects six of the buildings, find the probability that the first four buildings will pass the inspection and the remaining two will fail the inspection. Then find the probability that just four of the buildings will pass inspection. Round your answers to four decimal places, if necessary. ​ = __________ ​ = __________

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 11 or more of the accounts will be delinquent?

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.

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 times a die is thrown until a 3 appears. ​

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 3 mo. Find the probability that one of these hair dryers will last between 17 and 25 mo.

Sugar packaged by a certain machine has a mean weight of 4 lb and a standard deviation of 0.08 lb. For what values of c can the manufacturer of the machinery claim that the sugar packaged by this machine has a weight between and lb with probability at least 96%?

It is estimated that one third of the general population has blood type . If a sample of six people is selected at random, what is the probability that exactly three of them have blood type ? Round answer to three decimal places, if necessary. ​ __________ ​ What is the probability that at most three of them have blood type ? Round answer to three decimal places, if necessary. ​ __________

The probability distribution of a random variable X is Compute the mean, variance, and standard deviation of X.

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 failures in four trials of a binomial experiment in which p = The probability is __________.

A survey was conducted by the Public Housing Authority in a certain community among 1,000 families to determine the distribution of families by size. The results follow. Find the probability distribution of the random variable X, where X denotes the number of persons in a randomly chosen family. ​