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 probability that the time interval between two consecutive defective light bulbs will be less than 10 minutes?

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 less than 15 minutes?

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,the probability is 50% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

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.

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 less than 15 minutes?

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

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 within no sooner than 5 seconds after just being hit by a visitor?

The probability that a standard normal random variable,Z,falls between -2.00 and -0.44 is 0.6472.

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 between 2 and 12 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 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 between 25 and 30 computers that require repair on a given day using a normal approximation.

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 between 5 minutes and 15 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 between $1,200 and $1,600?

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 die before they reach the standard retirement age of 65?

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 $800 and $900?

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 less than $13,000?

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 fourteenth standard normal quantile is ________.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So 85% of the possible Z values are smaller than ________.

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 0.35 that John's income as a waiter is no less than how much in a given month?

Times spent watching TV every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends less than 20 hours watching TV is ________.

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 16 and 21 minutes.