Exam 6: The Normal Distribution and Other Continuous Distributions

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. -The probability that Z values are larger than _________is 0.3483.

The probability that a standard normal random variable,Z,is between 1.00 and 3.00 is 0.1574.

The amount of pyridoxine (in grams)in a multiple vitamin is normally distributed with $\mu$ = 110 grams and $\sigma$ 25 grams. -What is the probability that a randomly selected vitamin will contain between 100 and 110 grams of pyridoxine?

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 more than 11 minutes.

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?

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. -Find the waiting time at which only 10% of the customers will continue to hold.

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 income as a waiter is at least $1,400?

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

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 30.

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan.Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. -Find the age at which payments have ceased for approximately 86% of the plan participants.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. -The probability that Z is less than 1.15 is _________.

Instruction 6.5 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 6.5,the seventh standard normal quantile is _______

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 6.2 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 no more than $8,000?

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 less than 20 minutes.

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.

To determine the probability of getting at least 3 successes in a binomial distribution,you will find the area under the normal curve for X = 2.5 and above.

Instruction 6.1 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 6.1,a single Monday is chosen at random.State in which of the following ranges the number of column centimetres of classified advertisement is most likely to be

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,John's commission from the jewellery store will be between what two values symmetrically distributed around the population mean 90% of the time?

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 0.75 that John's commission from the jewellery store is less than how much in a given month?