Exam 6: The Normal Distribution and Other Continuous Distributions

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 variance of the time interval?

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the normal distribution is used for a discrete random variable while the binomial distribution is used for a continuous random variable.

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 14 and 16 minutes.

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 average time between consecutive hits?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour.What is the probability that a randomly chosen arrival to be more than 5 minutes?

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

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.

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 first standard normal quantile is ________.

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 0.6985.

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 $11,000 and $12,000?

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.So,17% of the products would be assembled within ________ minutes.

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.

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 between 82 and 100 grams of pyridoxine?

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 4.5 minutes will hang up before placing an order?

For some value of Z,the probability that a standard normal variable is below Z is 0.2090.The value of Z is

If a particular batch of data is approximately normally distributed,we would find that approximately

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because a random variable having a binomial distribution can have only a specified value while a random variable having a normal distribution can take on any values within an interval around that specified value.

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever np is at least 5.

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 between 10 and 20 minutes?

The value of the cumulative standardised normal distribution at Z is 0.6255.The value of Z is