Exam 6: The Normal Distribution and Other Continuous Distributions

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. -In the game Wheel of Fortune,which of the following distributions can best be used to compute the probability of winning the special vacation package in a single spin?

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 less than 8 computers that require repair on a given day using a normal approximation.

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 more than 25 computers that require repair on a given day using a normal approximation.

To determine the probability of getting between 2 and 4 successes in a binomial distribution,you will find the area under the normal curve between X = 1.5 and 4.5.

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,for a given month,what is the probability that John's income as a waiter is no more than $300?

If a data batch is approximately normally distributed,its normal probability plot would be S-shaped.

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,for a given month,what is the probability that John's income as a waiter is more than $900?

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 fifth standard normal quantile is ________.

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. -A catalogue company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes.What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

If we know that the length of time it takes a university student to find a parking space in the university car park follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute,find the point in the distribution in which 75.8% of the university students exceed when trying to find a parking space in the car park.

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 less than 304 cm?

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,for a given month,what is the probability that John's commission from the jewelry store is no more than $8,000?

Instruction 6-3 The number of column centimetres of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean 320 and population standard deviation 20 cm. -Referring to Instruction 6-3,for a randomly chosen Monday the probability is 0.1 that there will be less than how many column centimetres of classified advertisements?

Which probability distribution is skewed to the right,with the mean larger than the median?

A catalogue company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 2.8 minutes.What proportion of callers is put on hold longer than 2.8 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 at least 25 computers that require repair on a given day using a normal approximation.

Instruction 6-1 The manager of a surveying company believes that the average number of phone surveys completed per hour by her employees has a normal distribution.She takes a sample of 15 days' output from her employees and determines the average number of surveys per hour on these days.The ordered array for this data is: 10.0,10.1,10.3,10.5,10.7,11.2,11.4,11.5,11.7,11.8,11.8,12.0,12.2,12.2,12.5. -Referring to Instruction 6-1,the data appears reasonably normal but not perfectly normal.

The probability that a standard normal random variable,Z,is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.

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.A citation rainbow trout should be one of the top 2% in weight.Assuming the weights of rainbow trout are normally distributed,at what weight (in kilograms)should the citation designation be established?

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever np and n(1-p)are at least 5.