The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.43 and 0.95? (c) What is the probability of generating a number greater than 0.82? ... (a) Choose the correct graph of the uniform density function below. O A. O B. OC. ADensity 1.2- ADensity 1.2- 1- 0.8- 0.6- 0.4- 0.2- ADensity 1.2- 1- 1- 0.8- 0.6- 0.4- 0.2- 0.8- 0.6- 0.4- 0.2- 0- 0- o 0.2 0.4 0.6 0.8 i 1.2 0- o 0.2 0.4 0.6 0.8 i 1.2 ó 0.2 0.4 0.6 0.8 i 1.2 (b) The probability is (Simplify your answer.) (c) The probability is (Simplify your answer.)

Consider the random variable X with probability distribution (see image) Find a and E[X]

(b) Among fatal crashes when it is dawn/dusk, what is the probability that a randomly selected fatal crash occurs in unknown weather conditions? The probability that a randomly selected fatal crash when it is dawn/dusk occurs in unknown weather conditions is approximately. (Round to three decimal places as needed.) Data table Weather Normal Rain Snow/Sleet Other Unknown Daylight Dark, but Lighted 5875 14,307 875 219 125 810 497 51 54 255 Light Conditions Dark Print 8151 681 156 220 548 Dawn/Dusk Other Done 1183 87 17 40 71 65 8 2 9 133 0 - X

2. Is the graph shown a probability distribution (prob density function) of a continuous random variable? Why or why not? 1 0 1 2 4

A manufacturer guarantees a product for 1 year. The lifespan of the product after it is sold is given by the probability density function below, where t is time in months. ( See attachment) What is the probability that a buyer chosen at random will have a product failure A) During the warranty? B) During the second year after purchase?

Please answer this one. Thank you!

The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 2.1 times every two hours. The shopping center is open from 10 A.M. to 9 P.M. (11 hours). Let r be the number of shoplifting incidents caught by security in an 11-hour period during which the center is open. What is λ? (Use 2 decimal places.)(b) What is the probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security? (Use 4 decimal places.)(c) What is the probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security? (Use 4 decimal places.)

The wait time at a popular fast food restaurant is uniformly distributed between 2 and 10 minutes on average (a) Find the probability that you wait less than 4 minutes.  (b) Find the probability that you wait between 8 and 10 minutes. (c) Explain why the answers to (a) and (b) are the same. Hint: draw the probability density function for a Uniform random variable. Explain with a graph and also without a graph.

Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below. x 1 2 3 4 5 6 7 p(x) 0.04 0.05 0.09 0.24 0.36 0.14 0.08 (a) What is P(x = 4)? P(x = 4) = (b) What is P(x ≤ 4)? P(x ≤ 4) = (c) What is the probability that the selected student is taking at most five courses?   (d) What is the probability that the selected student is taking at least five courses?   (e) What is the probability that the selected student is taking more than five courses?

(a) Formulate a probability statement to determine the value of z so that the area under the standard normal curve in the right tail is 0.0330: P(Za) 0.0330 (b) Convert the probability statement relating to an area to the left of the normal curve: (c) Locate the closest probability value available in the standard normal table. Give the answer with four decimal places. The closest probability value i (d) Find the z value corresponding to the answer for (c). Give the answer with two decimal places. Z= P(Zsa)-0.967