Calculate the percentage of hours in which less than 2 customers enter the shop.
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1.The number of customers who enter a shop in an hour is Poisson distributed with a
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- Suppose the number of customers visiting a shoe store follows a Poisson process with a rate of 85 per day. Assume 55 percent of cus- tomers make a purchase. The amount spent by a paying customer follows an exponential distribution with a mean of $105. The two distributions are independent. What is the standard deviation of the total sales per day for the shoe store?18. On average, a banana will last 6.3 days from the time it is purchased in the store to the time it is too rotten to eat. Is the mean time to spoil greater if the banana is hung from the ceiling? The data show results of an experiment with 15 bananas that are hung from the ceiling. Assume that that distribution of the population is normal. 5.4, 8.2, 7.8, 6.8, 6.4, 8.3, 5, 7.5, 7, 5.3, 6.9, 8.8, 8.9, 9, 8.5 What can be concluded at the the αα = 0.05 level of significance level of significance? For this study, we should use T- Test, Z test The null and alternative hypotheses would be: H0: P or U, <>=, H1: P or U, <>=, The test statistic T,Z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is <> αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest that the population…Dffh
- 1. If X - N(200,2²), find а) Р(X < 197) b) Р(X < 200.5) 2. Let x be a continuous random variable that is normally distributed with a mean of 80 and a standard deviation of 12. Find the probability that x assumes a value a. greater than 69 c. greater than 101 b. less than 73 d. less than 87 3. Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value a. between 29 and 36 b. between 22 and 35 4. Let X denote the time taken to run a road race. X is normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race a. in less than 160 minutes? b. in 215 to 245 minutes?b. The compensation received by the highest-paid executives of 12 international companies (in $'000) is as follows: 801 820 2215 803 850 856 899 846 902 856 911 947 i. Find the mean and the median compensation of the executives. Comment on the skewness of the distribution of the executives' compensations. 26. Consider a coffee shop that uses a single-server queue. The inter-arrival time is exponentially distributed with a mean of 10 minutes and the service time is also exponentially distributed with a mean of 8 minutes. Calculate the: (i) mean wait in the queue (2) (ii) mean number in the queue (2) (iii) the mean wait in the system (2) (iv) mean number in the system (2) (v) proportion of time the server is idle. (2) [10] 7. The arrival of customers at a bank follows a Poisson distribution with a mean arrival rate of 10 customers per hour. The service time at the bank follows an exponential distribution with a mean service rate of 6 minutes per customer. Calculate the average number of customers in the system (including those being served and waiting) and the average time a customer spends in the system. How is the system performing? [8]
- 4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min11. Give an example of a set of data that satisfies the following conditions. has 8 data bimodal median = 10 mean = 10
- 2. Doctors volunteer their time on a daily basis in a clinic. The total number of patients served in a day at the clinic has mean 90 and variance 1890. Determine the probability that 120 or more patients can be served in a day at the clinic. Use the Central Limit Theorem with continuity correction. Use linear interpolation with the normal distribution to find the probability.8. The thickness of photoresist applied to wafers in semiconductor manufacturing at a particular location on the wafer is uniformly distributed between 0.2050 and 0.2150 micrometers. la) Determine the cumulative distribution function of photoresist thickness. (b) Determine the proportion of wafers that exceeds 0.2125 micrometers in photoresist thickness. (c) What thickness is exceeded by 10% of the wafers? (d) Determine the mean and variance of photoresist thickness.12. x: 471.7 659.3 740.5 790.5 781.3 1047.3 969.5 1206.1 y: 446.3 680.2 725.2 765.3 740.4 1005.6 936.3 1156.8 Using the data find the y mean 219.60 833.28 205.42 807.01
