Exam 6: The Normal Distribution and Other Continuous Distributions

A food processor packages orange juice in small jars.The weights of the filled jars are approximately normally distributed with a mean of 336 grams and a standard deviation of 9.6 grams.Find the proportion of all jars packaged by this process that have weights that fall above 350.4 grams.

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.The probability is ________ that a product is assembled in between 10 and 12 minutes.

The normal distribution is related to the Central Limit Theorem.

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.The probability is ________ that a product is assembled in between 15 and 21 minutes.

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,the probability that a randomly selected rainbow trout will weigh between 3 and 5 kilograms 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. -Referring to Instruction 6-2,the second standard normal quantile is ________.

Let X represent the amount of time it takes a student to park in the car park at the university.If we know that the distribution of parking times can be modelled using an exponential distribution with a mean of 4 minutes,find the probability that it will take a randomly selected student more than 10 minutes to park in the car park.

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,which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will require repair on a given day?

In its standardised form,the normal distribution

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 between $5,000 and $7,000?

To determine the probability of getting between 3 and 4 successes in a binomial distribution,you will find the area under the normal curve between X = 3.5 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 between $700 and $1,600?

Instruction 6-6 The interval between consecutive hits at a web site is assumed to follow an exponential distribution with an average of 40 hits per minute. -Referring to Instruction 6-6,what is the probability that the next hit at the web site will occur between the next 1.2 and 1.5 seconds after just being hit by a visitor?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1.5 patients per hour.What is the probability that a randomly chosen arrival to be less than 10 minutes?

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 at least $1,400?

Theoretically,the mean,median,and the mode are all equal for a normal distribution.

Any set of normally distributed data can be transformed to its standardised form.

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,construct a normal probability plot for the data.

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,what is the probability there will be between 280 and 360 column centimetres of classified advertisement?

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 standard deviation of the time interval?