8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable X that follows an exponential distribution with mean 15 minutes. a) Find P(14 < X < 22). Round off your answer to two decimal places. x 22 1 P(14 < X <22) = √₂/1² 15 e 15dx = P(x < 22) — P(x < 14) x 15 122 = e 15 22 1 - e 14 or 0.8 = = 22 14 = −e 15 + e15 = 0.16254≈ 0.16 - (1 – b) Find the 80th percentile. Round off to the nearest whole number. 1 X S 15 14 e 15 t e 15 dt X 0.8 = 1 e 15 X e 15 = = 0.2 14 22 = e 15 e 15 = 0.16 x — = ln (0.2). This gives x = 24.14156 15

8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable X that follows an exponential distribution with mean 15 minutes. a) Find P(14 < X < 22). Round off your answer to two decimal places. x 22 1 P(14 < X <22) = √₂/1² 15 e 15dx = P(x < 22) — P(x < 14) x 15 122 = e 15 22 1 - e 14 or 0.8 = = 22 14 = −e 15 + e15 = 0.16254≈ 0.16 - (1 – b) Find the 80th percentile. Round off to the nearest whole number. 1 X S 15 14 e 15 t e 15 dt X 0.8 = 1 e 15 X e 15 = = 0.2 14 22 = e 15 e 15 = 0.16 x — = ln (0.2). This gives x = 24.14156 15

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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3.1 - 3.5 Please solve for all
6. An optical device is used to detect the passage of cars in a single lane of a downtown street. Because there must be at least half a second between successive cars, it is assumed that the times T; between = 0.50 + Si, where S1, S2, ··. are independent exponential (A) random cars are of the form T; variables. (a) Find the mean and variance of each T;. (b) Let Y, be the time at which the nth car passes the detector. Calculate the mean and variance of Yn. (c) Under what conditions is Yn approximately normally distributed and why? (d) When n = 50 and A = 0.10, calculate the approximate probability that Yn exceeds 500 seconds.
When a man observed a sobriety checkpoint conducted by a police department, he saw 667 drivers were screened and 4 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W) = 0.00600, where W denotes the event of screening a driver and getting someone who is intoxicated. What does P (W) denote, and what is its value? What does P(W) represent? O A. P(W) denotes the probability of a driver passing through the sobriety checkpoint. O B. P(W) denotes the probability of driver being intoxicated. O C. P(W) denotes the probability of screening a driver and finding that he or she is not intoxicated. O D. P(W) denotes the probability of screening a driver and finding that he or she is intoxicated. P(W) =O (Round to five decimal places as needed.)
22
4.2 9
Ex: 4.1 I don’t know how they calculated the p(x) in table 4.1
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9. In t-test, if the resultant t value is -2.72 and p<.05, what is the interpretation? a. This test is statistically significant b. This test is not statistically significant c. It is unclear whether this is statistically significant or not d. not sure
parts of question 7. solve A-E A. Compute P(X = 3) for n = 5, p = 1 B. Ken is a waiter at a restaurant. His customers tip 15% or more 80% of the time. Find the probability that four of the next six customers will tip 15% or more? C. Find the z-score if x = 2.65, mean = 0, σσ = 1.0. D. An IQ test has a mean of 100 and standard deviation of 15. Find what percentile is someone who scored a 122 on an IQ score? E. A normal distribution has a mean of 168 and a standard deviation of 10. Find the percentage of scores that fall between 155 and 169.
8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable X that follows an exponential distribution with mean 15 minutes. a) Find P(14 < X < 22). Round off your answer to two decimal places. x 22 1 P(14 < X <22) = √₂/1² 15 e 15dx = P(x < 22) — P(x < 14) x 15 122 = e 15 22 1 - e 14 or 0.8 = = 22 14 = −e 15 + e15 = 0.16254≈ 0.16 - (1 – b) Find the 80th percentile. Round off to the nearest whole number. 1 X S 15 14 e 15 t e 15 dt X 0.8 = 1 e 15 X e 15 = = 0.2 14 22 = e 15 e 15 = 0.16 x — = ln (0.2). This gives x = 24.14156 15
7.54 A random variable is Poisson distributed with A = 0.50 arrivals per minute. For the corresponding exponential distribution, and x = minutes until the next arrival, identify the mean of x and determine the following: a. P(x S 0.5) b. P(x S1.5) с. Р\х 2.5) d. P(x 3.0)