Exam 6: The Normal Distribution and Other Continuous Distributions

The value of the cumulative standardised normal distribution at Z is 0.8770.The value of Z is

The "middle spread",that is the middle 50% of the normal distribution,is equal to one standard deviation.

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 at least 80 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 less than 2.2 kilograms is ________.

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,John's commission from the jewelry store will be between what two values symmetrically distributed around the population mean 80% of the time?

For some positive value of Z,the value of the cumulative standardised normal distribution is 0.8340.The value of Z is

The amount of pyridoxine (in grams)in a multiple vitamin is normally distributed with μ = 110 grams and σ= 25 grams.What is the probability that a randomly selected vitamin will contain at least 100 grams of pyridoxine?

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes.What is the average number of arrivals per minute?

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 0.45 that John's income as a waiter is more than how much in a given month?

To determine the probability of getting fewer than 3 successes in a binomial distribution,you will find the area under the normal curve for X = 3.5 and below.

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 25 or more than 30 computers that require repair on a given day using a normal approximation.

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 at least 50 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. -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.

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.What proportion of the plan recipients would receive payments beyond age 75?

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 fourth 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 between 301 and 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,John's income as a waiter will be between what two values symmetrically distributed around the population mean 80% of the time?

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

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 but less than 30 computers that require repair on a given day using a normal approximation.

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.