Question

Let ? be the number of female customers who arrive at a barber shop before the...

Let ? be the number of female customers who arrive at a barber shop before the first male customer arrives. The probability of a female customer arriving at the barber shop is 0.75.

(i) Find ?(? ≥ 8).

(ii) In a random sample of size 36, find the normal approximation for ?(2.5 ≤ ?̅ ≤ 3.5), where ?̅ is the sample mean.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Customers arrive at Lily’s Barber Shop during a day in any particular business hour according to...
Customers arrive at Lily’s Barber Shop during a day in any particular business hour according to a Poisson distribution with a rate of ? = 2 per hour. Now the shop has two barbers who can each service a customer in exactly 15 minutes. Suppose a customer, Lisa, arrives at 3:00pm and finds both barbers idle. Find (i) The probability that we will observe customers waiting before 3:15pm. (ii) The probability that Lisa will find the shop empty when she...
Individual customers arrive at a coffee shop after it opens at 6 AM. The number of...
Individual customers arrive at a coffee shop after it opens at 6 AM. The number of customers arriving by 7AM has a Poisson distribution with parameter λ = 10. 25% of the customers buy a single donut and coffee, and 75% just buy coffee. Each customer acts independently. Answer the following: a.What are the two random variables described above and what are their probability mass functions? b.What is the probability that exactly five customers arrive by 7AM? c.If 10 customers...
Customers arrive at a shop at the rate of 7 per 10-minute interval. what is the...
Customers arrive at a shop at the rate of 7 per 10-minute interval. what is the probability that we need to wait at least 10 minutes before the next customer arrives at the shop? Obtain the probability using Poisson distribution and Exponential distribution.
A grocery store counts the number of customers who arrive during an hour. The average over...
A grocery store counts the number of customers who arrive during an hour. The average over a year is 20 customers per hour. Assume the arrival of customers follows a Poisson distribution. (It usually does.) Find the probability that at least one customer arrives in a particular one minute period. Round your answer to 3 decimals.     Find the probability that at least two customers arrive in a particular 4 minute period. Round your answer to four decimals.
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that...
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that the number of customer arrivals X follows a Poisson distribution. Find the probability of more than 25 people arriving within the next two hours using the Poisson mass function. Find the probability of more than 25 people arriving within the next two hours using the normal approximation to the Poisson. Compute the percent relative difference between the exact probability computed in part 1 and...
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that...
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that the number of customer arrivals X follows a Poisson distribution. 1. Find the probability of more than 25 people arriving within the next two hours using the Poisson mass function. 2. Find the probability of more than 25 people arriving within the next two hours using the normal approximation to the Poisson. 3. Compute the percent relative difference between the exact probability computed in...
Four cashiers are on duty in a bank where customers may be assumed to arrive independently...
Four cashiers are on duty in a bank where customers may be assumed to arrive independently and at random, at an average rate of 60 per hour. If a cashier is free, then an arriving customer receives immediate attention; otherwise a central queue is formed. The service time for each cashier may be assumed to be exponentially distributed with mean 2 minutes. The traffic intensity  is . Assume that the queue is in equilibrium What is the probability that at any...
Arnold’s Muffler Shop has a top mechanic who can install mufflers at an average rate of...
Arnold’s Muffler Shop has a top mechanic who can install mufflers at an average rate of 3/hour. Customers needing service arrive at the shop on the average of 2/hour. Assuming the standard assumptions of queueing models exist, find the following: The utilization of the mechanic The probability that there are 0 customers in the system, 2 customers in the system. The average number of customers in line The average time a customer waits before getting a new muffler The average...
Let p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to...
Let p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to nuts. Let n1,n2 be the sample size of a random sample for male and female, respectively. Assume two samples are indepedent. Let X1,X2 be the number of male and female who have allergy to nuts in the random sample, respectively. (1)(3pts) For parameters p1,p2, and p1−p2, find one unbiased estimator for each of them. And show why they are unbiased. (2)(3pts) Derive the formula...
Let p1,p2p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to...
Let p1,p2p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to nuts. Let n1,n2n1,n2 be the sample size of a random sample for male and female, respectively. Assume two samples are indepedent. Let X1,X2 be the number of male and female who have allergy to nuts in the random sample, respectively. (1)(3pts) For parameters p1,p2,p1,p2, and p1−p2p1−p2, find one unbiased estimator for each of them. And show why they are unbiased. (2)(3pts) Derive the formula...