zoriahmendoza
17.03.2020 •
Mathematics
Customers make purchases at a convenience store, on average, every fourteen minutes. It is fair to assume that the time between customer purchases is exponentially distributed. Jack operates the cash register at this store.
a-1. What is the rate parameter
λ
? (Round your answer to 4 decimal places.)
Rate parameter
λ
a-2. What is the standard deviation of this distribution? (Round your answer to 1 decimal place.)
Standard deviation
b. Jack wants to take a ten-minute break. He believes that if he goes right after he has serviced a customer, he will lower the probability of someone showing up during his ten-minute break. Is he right in this belief?
Yes No
c. What is the probability that a customer will show up in less than ten minutes? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)
Probability
d. What is the probability that nobody shows up for over forty minutes? (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)
Probability
Solved
Show answers
More tips
- H Health and Medicine How to Lower Your Child s Temperature?...
- F Food and Cooking From Latte to Espresso: Which Coffee Drink is the Most Popular on Earth?...
- C Computers and Internet How to Set Up Internet on iPhone? Detailed Guide with Step-by-Step Instructions...
- P Philosophy 8 привычек, чтобы достичь счастливой жизни...
- F Food and Cooking How Many Grams Are In a Tablespoon?...
- G Goods and services How to Choose the Right Iron: Purchase Tips...
- S Style and Beauty How to Choose the Perfect Hair Straightener?...
- H Health and Medicine How to Choose the Right Glasses?...
- H Health and Medicine What vaccines do children need?...
- H Health and Medicine AKDS Vaccination: Ensure Your Child s Safety...
Answers on questions: Mathematics
- M Mathematics What is 871,495 rounded to the nearest thousand?...
- M Mathematics James and theresa are raising money by selling candy bars at school. james has already saved up $12 on his own and he decides to sell the candy bars for $2 each. theresa didn...
- H History Who invented interchangeable parts...
- M Mathematics Help i will give brainiest...
Ответ:
The answers to the questions are;
a-1. The rate parameter, λ is 0.0714 .
a-2. The standard deviation is 14.
b. No
c. The probability that a customer will show up in less than ten minutes is 0.5104.
d. The probability that nobody shows up for over forty minutes is 0.0574.
Step-by-step explanation:
a-1. The exponential distribution probability density function is given by
PDF = and the cumulative distribution function is given by
CDF =
Therefore the rate parameter the rate at which customers make purchases, that is the number of customers per minute
Therefore, the number of customers per minute = rate parameter = 1/14
The rate parameter, λ = 0.0714 .
a-2. In exponential distribution, which is the probability of the amount of time between two events where the rate of occurrence of events is constant, known as a Poisson point process, we have;
The mean = 1/λ = standard deviation
Therefore, the standard deviation is 14.
b. No
c. The probability that a customer will show up in less than ten minutes is given by the cumulative distribution function as follows
P (10<X) = = 0.5104.
d. The probability that nobody shows up for over forty minutes is given by the area on the right of the exponential distribution function curve.
Therefore, we have
P (X>40) = = 0.0574
The probability that nobody shows up for over forty minutes is 0.0574.
Ответ: