The amount of time required to serve a customer at a fast food restaurant has an exponential density function with mean 4 minutes. Find the probability that a customer is served in less than 1 minute.The probability that a customer is served in less than 1 minute is(Type an exact answer.)

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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State the two characteristics of the graph of a probability density function. Complete the statements below. 1. The total area under the graph of the equation over all possible values of the random variable must ▼ equal 1. be positive. equal 0. 2. The height of the graph of the equation must be ▼ less than or equal to 1 greater than or equal to 0 between 0 and 1, inclusive, for all possible values of the random variable.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant с 239 32 A B 318 273 53 D 147 12 Order Accurate Order Not Accurate 39 If one order is selected, find the probability of getting food that is not from Restaurant A. The probability of getting food that is not from Restaurant A is (Round to three decimal places as needed.)
Assume that the time it takes for bacterial growth on a dairy product after it is taken out of fridge follows an Exponential distribution with a mean of 10 minutes. What is the probability that bacterial growth will not happen in 15 minutes if the dairy product has already been out of the fridge for 10 minutes? O A. 0.393 O B. 0.777 O C. 0.607 O D. 0.223 Reset Selection
An electronic scale at an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.02 and fills are independent. Determine the probability mass function of the number of fills (x) before the manufacturing line is stopped.
During peak hours, the arrival of customers at a fast food restaurant is random with an average rate of 75 customers per hour. Find the probability that a. 20 people will arrive at a 15-minute period. b. A maximum of 175 people will arrive at a 2-hour period.
The time (in hours) until the next emergency arrival at a hospital follows an exponential distribution with a mean of 2.1 What is the probability that exactly 4 emergencies arrive in the next ten hours? (Assume arrival times are independent of each other.) What is the probability that at least four emergencies arrive within the next 10 hours?
Because all airline passengers do not show up for their reserved sear an airline sells n=125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10 assume that the passengers behave independently.
The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of $204. a. The lambda of this distribution is b. The probability that the cost is larger than $238 is P(x > $238) = c. The probability that the cost is less than $76 is P(x s $76) = d. The probability that the cost is between $185 and $244 is P($185 s x < $244) = e. The 61st percentile is cost of maintenance s
. Let the waiting time 'w' has a gamma distribution with a = k and b = 12. Write the corresponding probability density function and also obtain the average waiting time.
The time it takes to complete an online survey is uniformly distributed over the range of 10.1 minutes to 16 minutes. Calculate the probability that it takes a person between 11.2 and 11.9 minutes to complete the survey.
Let random variable X denote the length of a wire, assumed to be exponentially distributed with mean 107 cm. The wire is cut to make rings of radius 1 cm. Derive the probability mass function for the number of complete rings that can be produced by each length of wire.
Assume that the machine yields the item selected 90 percent of the time, and returns nothing 10 percent of the time. Three individuals attempt to use the machine. Let X be defined as the number of individuals who obtain the item selected. How many different values are possible for the random variable X? Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order.

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The amount of time required to serve customer at a fast food restaurant has an exponential density function with mean 4 minutes. Find the probability that a customer is served in less than 1 minute. C... The probability that a customer is served in less than 1 minute is (Type an exact answer.)