Exam 6: The Normal Distribution and Other Continuous Distributions

Instruction 6.6 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 6.6,what is the probability that the time interval between two consecutive defective light bulbs will be at least 90 minutes?

The Townsville International Airport (TIA)has been criticised for the waiting times associated with departing flights.While the critics acknowledge that many flights have little or no waiting times,their complaints deal more specifically with the longer waits attributed to some flights.The critics are interested in showing,mathematically,exactly what the problems are.Which type of distribution would best model the waiting times of the departing flights at TIA?

Instruction 6.4 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 6.4,construct a normal probability plot for the data.

Instruction 6.2 John has two jobs. For daytime work at a jewellery 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 6.2,for a given month,what is the probability that John's commission from the jewellery store is less than $13,000?

To determine the probability of getting no more than 3 successes in a binomial distribution,you will find the area under the normal curve for X = 2.5 and below.

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

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 6.4 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 6.4,the data appear reasonably normal but not perfectly normal.

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,15% of the products require more than_________minutes for assembly.

A normal probability plot may be used to assess the assumption of normality for a particular batch of data.

The probability that a standard normal random variable,Z,is below 1.96 is 0.4750.

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?

A food processor packages green olives 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 below 348 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.

Instruction 6.8 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 6.8,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 two computers will require repair on a given day?

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

Instruction 6.2 John has two jobs. For daytime work at a jewellery 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 6.2,the probability is 0.25 that John's income as a waiter is no more than how much in a given month?

Times spent using a tablet or smartphone every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends more than 5 hours using a tablet or smartphone is _______

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.

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 15.