Exam 8: Probability Distributions

Find the mean and standard deviation of the number of tails obtained in 576 flips of a balanced coin using the fact that $\mathrm{x}$ is a binomial random variable. If necessary, round to the nearest thousandth.

Tell whether the given function can serve as the probability distribution of an appropriate random variable. -=0.25, f(2)=0.40, f(3)=0.30\)

The use of the Poisson distribution requires a value $n$ which indicates a definite number of independent trials.

The mean of a Poisson distribution is given by _______.

The number of monthly breakdowns of a conveyor belt at a local factory is a random variable having the Poisson distribution with $\lambda=2.8$ . -Find the probability that the conveyor belt will function for a month with two breakdowns. Round to the nearest thousandth.

A service station receives an average of six customers per hour. The probability that there will be three arrivals in a given hour can be found by using the

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -At least three bounce.

If we want to calculate the probability of from four to six successes in a hypergeometric distribution problem, then we must use the formula three times.

It has been found that $40 \%$ of the employees who complete a sequence of executive seminars go on to become vice presidents. Assume that 10 graduates of the program are randomly selected. -In the situation above, find the probability that no one becomes a vice president.

If a binomial distribution problem has $\mathrm{p}=0.003$ and $\mathrm{n}=1000$ , then the answer should be approximated by using

A company produces stereo components. The probability of the company producing a defective component is 0.003 . -In the situation above, if 1000 components are produced, find the probability that at most 4 components are defective.

A company produces stereo components. The probability of the company producing a defective component is 0.003 . -In the situation above, if 1000 components are produced, find the probability that from 4 to 6 components are defective.

Three companies share the entire market for a particular product. Company A has a $50 \%$ share, company B has a $\mathbf{3 0} \%$ } share, and company $\mathrm{C}$ has a $20 \%$ . -If 12 people who buy the product are selected at random, find the probability that five buy the product from company A, four from company B, and three from company C.

If we apply Chebyshev's theorem to the 60 to 80 interval of distribution, with $\sigma=5$ , the value of $\mathrm{k}$ will be _______.

The standard deviation is a measure of the theoretical average value that a distribution is likely to assume for a large number of trials.

A die is rolled 10 times. The probability of obtaining from 4 to 7 threes should be determined using the formula for the

Check whether the condition for the binomial approximation to the hypergeometric distribution is satisfied if a $=230, \mathrm{~b}=290$ , and $\mathrm{n}=27$ .

Which of the following can be probability distributions? Justify your answer. a. $f(1)=0.40, f(2)=0.20, f(3)=0.50$ where the random variable can take on only the values 1,2 , and 3 . b. $f(x)=x / 10$ for $x=0,1,2,3,4$ . c. $f(1)=0.25, f(2)=0.30, f(3)=0.15, f(4)=0.15$ where the random variable can take on only the values $1,2,3$ and 4 . d. $f(x)=\frac{x-3}{7}$ for $x=0,1,2,3,4,5$