Exam 6: The Normal Distribution and Other Continuous Distributions

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

Which probability distribution is skewed to the right,with the mean larger than the median?

Instruction 6.7 The interval between consecutive hits at a website is assumed to follow an exponential distribution with an average of 40 hits per minute. -Referring to Instruction 6.7,what is the average time between consecutive hits?

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 last 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,the probability is 0.30 that John's commission from the jewellery store is no more than how much in a given month?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. -So 96% of the possible Z values are between _________and _________ (symmetrically distributed about the mean).

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?

When p is not equal to 0.5,the binomial distribution is not symmetrical; however,the closer the p is to 0.5 and the larger the sample size,the more symmetrical the distribution 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 probability that the time interval between two consecutive defective light bulbs will be exactly 10 minutes?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. -The probability that Z is between -2.33 and 2.33 is _________.

If we know that the length of time it takes a university student to find a parking space in the university car park follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute,find the probability that a randomly selected university student will find a parking space in the car park in less than 3 minutes.

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 less than 304 cm?

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 at least 80 minutes?

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 second 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 is less than -2.20 is _________.

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 more than 1 hour?

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 first standard normal quantile is ________.

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.A citation rainbow trout should be one of the top 2% in weight.Assuming the weights of rainbow trout are normally distributed,at what weight (in kilograms)should the citation designation be established?

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 $800 and $900?

The normal distribution is related to the Central Limit Theorem.