A quality characteristic is monitored by a control chart designed so the probability that an out-of-control condition will be detected on the first sample following the shift is 1 – ß. Find the following: th (a) The probability that the out-of-control condition will be detected on the n' sample following the shift. (b) The expected number of samples analyzed until the shift is detected. (c) The probability that the first sample following the shift produces a statistic that plots inside the control limits. (d) The probability of detecting the shift after the nth sample following the shift, which means the shift is detected in the (n+1)th, or (n+2) th, .... sample (e) The probability that n consecutive samples produce statistics that plot outside of the control limits.

If arrivals occur at a mean rate of 2.6 events per minute the exponential probability of waiting more than 1.5 minutes for the next arrival is is a .0202 or .0122 or .0535 or .2564

The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

Suppose a life insurance company sells a ​$170,000 ​1-year term life insurance policy to a 20​-year-old female for ​$170. According to the National Vital Statistics​ Report, 58(21), the probability that the female survives the year is 0.999544. The expected value of this policy to the insurance company is ​$92.48. What is the standard deviation of the value of the life insurance​ policy? Why is the value so​ high?

Suppose the horses in a large stable have a mean weight of 873lbs, and variance of 17,161. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 50 horses are sampled at random from the stable? Round your answer to four decimal places.

Suppose that in a large population of women (aged 20 to 29-years-old) that the mean serum cholesterol level is 183 mg/dl and the standard deviation is 37. Find the probability that a sample of size 60 from this population will yield a mean cholesterol level.   Greater than 190

A production line in a factory, assembles laptops. A random sample of assembly time of 36 laptops has been drawn from this factory. Suppose, the population distribution has a mean assembly time of 25 minutes and standard deviation 6 minutes. What is the probability that a sample mean is 26 minutes? Select one: a. 0.0 b. =P(Z>1) c. =P(Z=0) d. =P(Z<1) e. None of the others

The average amount of time until a car accident on a particular 60 mile stretch of road is 30 minutes. Assume(unreasonably) that car accidents are independent, the time to a car accident is exponentially distributed, and that two accidents cannot occur at the same time. a. What is the probability of a car accident occurring in the first hour?b. What is the probability of a car accident occurring between 15 and 45 minutes? c. What is the variance of the time until a car accident occurs? If a car accident has not happened in 2 hours, what is the probability it will happen in the next hour?   DO NOT USE THE INTEGRATION METHOD PLEASE.

A supervisor at a local widget making company has been monitoring the output of one of the machines used to manufacture small aluminum plates. Past data indicate that if the machine is operating "properly," the length of the plates produced by this machine can be modeled as being normally distributed with a mean of 117 centimeters and a standard deviation of 5.2 centimeters. Suppose 16 plates produced by this machine are randomly selected. What is the probability that the average length of these 16 plates will be between 116 and 120 centimeters when the machine is operating "properly?" Z and t TABLES ARE GIVEN AS QUESTIONS 28-29. PLEASE SHOW ALL YOUR CALCULATIONS.CORRECT ANSWER WITHOUT CALCULATIONS WILL BE AWARDED PARTIAL CREDIT. Paragraph В I