Exam 6: The Normal Distribution and Other Continuous Distributions

Scientists in the Amazon are trying to find a cure for a deadly disease that is attacking the rain forests there.One of the variables that the scientists have been measuring involves the diameter of the trunk of the trees that have been affected by the disease.Scientists have calculated that the average diameter of the diseased trees is 42 centimetres.They also know that approximately 95% of the diameters fall between 32 and 52 centimetres and almost all of the diseased trees have diameters between 27 and 57 centimetres.When modelling the diameters of diseased trees,which distribution should the scientists use?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So 96% of the possible Z values are between ________ and ________ (symmetrically distributed about the mean).

Instruction 6-4 John has two jobs.For daytime work at a jewelry store he is paid $15,000 per month,plus a commission.His monthly commission is normally distributed with mean $10,000 and standard deviation $2,000.At night he works as a waiter,for which his monthly income is normally distributed with mean $1,000 and standard deviation $300.John's income levels from these two sources are independent of each other. -Referring to Instruction 6-4,the probability is 0.30 that John's commission from the jewelry store is no more than how much in a given month?

Instruction 6-4 John has two jobs.For daytime work at a jewelry store he is paid $15,000 per month,plus a commission.His monthly commission is normally distributed with mean $10,000 and standard deviation $2,000.At night he works as a waiter,for which his monthly income is normally distributed with mean $1,000 and standard deviation $300.John's income levels from these two sources are independent of each other. -Referring to Instruction 6-4,the probability is 0.10 that John's commission from the jewelry store is more than how much in a given month?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be more than 1 hour?

Instruction 6-2 The city manager of a large city believes that the number of reported accidents on any weekend has a normal distribution.She takes a sample of nine weekends and determines the number of reported accidents during each.The ordered array for this data is: 15,46,53,54,55,76,82,256,407. -Referring to Instruction 6-2,the sixth standard normal quantile is ________.

The true length of boards cut at a mill with a listed length of 3 metres is normally distributed with a mean of 303 cm and a standard deviation of 1 cm.What proportion of the boards will be over 305 cm in length?

The owner of a fish market determined that the average weight for a rainbow trout is 3.2 kilograms with a standard deviation of 0.8 kilogram.Assuming the weights of rainbow trout are normally distributed,above what weight (in kilograms)do 89.80% of the weights occur?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is more than 0.77 is ________.

Suppose that past history shows that 60% of university students prefer Coca-Cola.A sample of 10,000 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola?

Instruction 6-5 Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. -Referring to Instruction 6-5,what is the probability that the time interval between two consecutive defective light bulbs will be exactly 10 minutes?

Instruction 6-2 The city manager of a large city believes that the number of reported accidents on any weekend has a normal distribution.She takes a sample of nine weekends and determines the number of reported accidents during each.The ordered array for this data is: 15,46,53,54,55,76,82,256,407. -Referring to Instruction 6-2,the data appears normal.

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes.So,70% of the products would be assembled within ________ minutes.

Instruction 6-7 A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15. -Referring to Instruction 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be exactly 10 computers that require repair on a given day using a normal approximation.

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be less than 20 minutes?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is between -2.33 and 2.33 is ________.

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.A batch of 100,000 such alarms was produced by independent production lines.Which of the following distributions would you use to figure out the probability that at least 90,000 of them will function properly in case of a fire?

The value of the cumulative standardised normal distribution at 1.5X is 0.9332.The value of X is

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes.What is the probability that a randomly chosen arrival to be more than 18 minutes?