Question 1. Exponential Probability Distributions ( (Exercise 6.29) The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. a. Sketch this exponential probability distribution. b. What is the probability that the arrival time between vehicles is 12 seconds or less? c. What is the probability that the arrival time between vehicles is 6 seconds or less? d. What is the probability of 30 or more seconds between vehicle arrivals?

Calls arrive at a switchboard a mean of one every 39 seconds. What is the exponential probability that it will take more than 29 seconds but less than 34 seconds for the next call to arrive?

Directions: During a certain part of the day, the time between arrivals of automobiles at the tollgate on a turnpike is an exponential random variable with expected value 30 seconds. 1. Find the probability that the time between successive arrivals is more than 70 seconds. Probability = 2. Find the probability that the time between successive arrivals is greater than 10 seconds and less than 50 seconds. Probability =

The amount of time, T, that the effect of caffeine is felt on your body after drinking a cup of coffee is given by a continuous random variable with an exponential distribution. On average, caffeine is felt for about 5 hours after drinking the cup. (Answer part a-c) a. What is the probability that the effect lasts at least 4 hours? b.  What is the probability that the effect lasts fewer than 6 hours? c.  You usually go to sleep at 11:30 pm, and drink exactly one cup of coffee a day. Suppose you wish to guarantee at most a 5% chance of feeling the effects of caffeine when you go to sleep. What's the latest that you should drink your only cup of coffee?

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6. A lightbulb will work until failure. Being a cheap Chinese import the lightbulb has a 0.001 chance of failure each time you turn on the lightbulb. We can think of failure when you turn on the lights as a Geometric Distribution A. What is a "success" for this Geometric Distribution? B. Find the probability of "success" or p for this Geometric Distribution. C. Find the probability of "not success" or q

K The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions. Complete parts (a) through (c) below. Click the icon to view the data for fatal crashes in 2016. (a) Among fatal crashes in unknown weather conditions, what is the probability that a randomly selected fatal crash occurs when it is dawn/dusk? The probability that a randomly selected fatal crash in unknown weather conditions occurs when it is dawn/dusk is approximately. (Round to three decimal places as needed.) Data table Weather Daylight Dark, but Lighted 5875 497 51 54 255 Normal Rain Snow/Sleet Other Unknown 14,307 875 219 125 810 (...) Dark 8151 681 156 220 548 Dawn/Dusk Other 1183 87 40 71 65 8 2 9 133 X