Exam 6: The Normal Distribution and Other Continuous Distributions

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 0.95 that John's commission from the jewellery store is at least how much in a given month?

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 data appear normal.

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 variance of the time interval?

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 fourteenth standard normal quantile is _______

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 no more than $300?

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,the probability is 75% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. -The probability that Z is more than 0.77 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,which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than two computers will require repair on a given day?

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.

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?

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,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?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. -The probability that Z is between -2.89 and -1.03 is _________.

The probability that a standard normal random variable,Z,falls between −1.50 and 0.81 is 0.7242.

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 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 fourth standard normal quantile is_______

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,for a randomly chosen Monday,what is the probability there will be less than 340 column centimetres of classified advertisement?

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 probability that a standard normal random variable,Z,is less than 50 is approximately 0.

To determine the probability of getting between 3 and 4 successes in a binomial distribution,you will find the area under the normal curve between X = 3.5 and 4.5.

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 more than 4.4 kilograms is_________.