TOPIC: Using Central limit theorem to find the sampling distribution of the sample mean and then to find the required probability.


6. Daily sales at a gas station are assumed to be independent of one another with...
A review of the sales records for Kim’s Karwash indicates that daily revenue can be represented by a normal distribution with mean of $2000 and standard deviation of $400. a. What is the probability that tomorrow’s profit will be greater than $2500? (Be sure to indicate the relevant Z-score(s) for the problem). B. What is the probability that profits fall between $1700 and $2300? (Be sure to indicate the relevant Z-score(s) for the problem). c. Suppose one day’s revenue is...
The daily sales of a certain variety store are approximately normally distributed with a mean of $10000 and a standard deviation of $2000. What is the probability that a random sample of 100 days will yield a mean greater than $9800?
1. A gas station opens at a time which is Normally distributed with the mean of 8:45 am and standard deviation of 10 minutes; similarly, its closing time is Normally distributed with the mean value at 5:12 pm and standard deviation of 15 minutes. If customers arrive as a Poisson Process with an average rate of 11.3 per hour, find the mean number of customers to be served in one such day, and the corresponding standard deviation. What is the...
4-87. Hits to a high-volume Web site are assumed to follow a Poisson distribution with a mean of 10,000 per day. Approxi- mate each of the following: (a) Probability of more than 20,000 hits in a day (b) Probability of less than 9800 hits in a day (c) Value such that the probability that the number of hits in a day exceeds the value is 0.01 (d) Expected number of days in a year (365 days) that exceed 10.200 hits....
9. A local fast-food restaurant finds that its daily profit has mean μ =50 dollars and standard deviation σ =100 dollars. If an auditor randomly selects 30 days, what is the probability that the average profit of the 30 days is a loss (i.e., average profit is less than 0)? (4pts)
At a certain fire station, false alarms are received at a mean rate of .2 per day. In a year, what is the probability that fewer than 52 false alarms are received? Note: You may need to use Excel to calculate the exact probability if the z-score is not in the book's tables. (Consider 365 days a year. Round your standard deviation value to 3 decimal places and z-value to 2 decimal places. Round your final answer to 4 decimal...
You are responsible for production and sales of Bosporus takeaway snacks. Daily production of snacks is normally distributed, with a mean of 40 and a variance of 100. Daily sales are also normally distributed, with a mean of 40 and a standard deviation of 6. Sales and production have a correlation of 0.50. The selling price per snack is $7. The variable production cost per snack is $3 The fixed production costs per day are $120. What is the probability...
Need problem solving process and the steps
version 3 Questions 09 - 10 To open a new gas station, a research to estimate the demand is conducted. According to the results, the daily demand for gas at the gas station measured in gallons would be normally distributed with a mean of 1,000 gallons and a standard deviation of 100 gallons. Q09 A concern is the possibility of too low demand. What is the value that fills the blank in the...
Daily sales 325 units Std. deviation of daily demand 39 Cost to place an order $30 Freight cost $250 Avg. Inventory (last 12 months) 2,750 units Cost of 1 unit of inventory $125 Cost of Goods Sold $14,828,125 Selling price of 1 unit $250 Avg. replenishment cycle 11 days Average inventory value $343,750 Re-stock fee is $55 Cost of capital = 22.5% Inventory Risk = 1.5% Storage space 5.5% =0.75% Insurance Current number of warehouses = 24 Prime interest rate...
Problem 2 A local service station is open 365 days per year. Sales of 10W40 premium engine oil averages . Inventory holding cost are $0.50 per can per year. Ordering cost are $10 per order. Lead time to deliver the order is 2 weeks. Backorders are not practical as the customer will chose another service station if the desired number of oil cans is not available immediately. 20 cans per day a. Based on these data chose the appropriate inventory...