Exam 6: The Normal Distribution and Other Continuous Distributions

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 worker earns $15 per hour at a company and is told that only 2.5% of all workers make a higher wage.If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour,the average wage for the company is $7.50 per hour.

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 first standard normal quantile is _______

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 mean of the time interval?

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 80% of the time?

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 sixth standard normal quantile is _______

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 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 6.6 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 between 10 and 35 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 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 exactly 10 computers that require repair on a given day using a normal approximation.

When constructing a normal probability plot,the Z values are plotted on the vertical axis and the corresponding values of the variable are plotted on the horizontal axis.

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be less than 20 minutes?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. -So 50% of the possible Z values are between _________and _________ (symmetrically distributed about the mean).

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 is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?

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

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.

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 _________

The exponential and Poisson distributions are closely related.

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 between $700 and $1,600?

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 at least $12,000?

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 ninth standard normal quantile is_______